Tom Robbins WW Prob Lib2 Summer 2001 WeBWorK assignment Algebra1RealNumbers due 1/4/05 at 2:00 AM.

Transcription

1 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment AlgebraRealNumbers due /4/05 at :00 AM..( pt) Evaluate the epression (Your answer cannot be an algebraic epression. ).( pt) Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false. You must get all of the answers correct to receive credit π 46.( pt) Match the statements defined below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit.. is greater than -. is greater than or equal to -. is any real number 4. The distance from to - is more than 5. The distance from to - is less than or equal to A. B. C. D. E. 4.( pt) Match the statements defined below with the letters labeling their equivalent intervals. You must get all of the answers correct to receive credit A. 8 B. 8 C. 8 D. E.

2 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment AlgebraPowers due /5/05 at :00 AM..( pt) Evaluate the epression 5. [NOTE: Your answer cannot be an algebraic epression. ].( pt) Evaluate the epression 4. [NOTE: Your answer cannot be an algebraic epression. ].( pt) Evaluate the epression [NOTE: Your answer cannot be an algebraic epression. ] 4.( pt) Evaluate the epression 4. [NOTE: Your answer cannot be an algebraic epression. ] 4. 5.( pt) Evaluate the epression 4 [NOTE: Your answer cannot be an algebraic epression. ] 4. 6.( pt) Evaluate the epression [NOTE: Your answer cannot be an algebraic epression. ] 7.( pt) Evaluate the epression 5. [NOTE: Your answer cannot be an algebraic epression. ] 8.( pt) Evaluate the epression 5 9. [NOTE: Your answer cannot be an algebraic epression.] 9.( pt) Evaluate the epression 5 5. [NOTE: Your answer cannot be an algebraic epression. ] 0.( pt) Evaluate the epression 7 4. [NOTE: Your answer cannot be an algebraic epression. ].( pt) The epression equals n where n is:.( pt) The epression a 5 b 4 c a b 5 c 5 equals na r b s c t where n, the leading coefficient, is: and r, the eponent of a, is: and s, the eponent of b, is: and finally t, the eponent of c, is: [NOTE: Your answers cannot be algebraic epressions.].( pt) The epression y z 5 5 y 5 z y equals r y s z t where r, the eponent of, is: and s, the eponent of y, is: and finally t, the eponent of z, is: [NOTE: Your answers cannot be algebraic epressions.] 4.( pt) The epression 4 y 5 y 5 4 equals r y s where r, the eponent of, is: and s, the eponent of y, is: 5.( pt) The epression y 4 y 5 5 equals r y s where r the eponent of is: and s the eponent of y is: 6.( pt) The epression 64 5 equals n r where n, the leading coefficient, is: and r, the eponent of, is: [NOTE: Your answers cannot be algebraic epressions.] 7.( pt) If you rationalize the denominator of then you will get 5 4 r 5 s n where r, s, and n are all positive integers (with no common factors). r s n [NOTE: Your answers cannot be algebraic epressions.] 8.( pt) Find if

3 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment AlgebraEpressions due /6/05 at :00 AM..( pt) The epression 4 7 equals A B where A equals: and B equals: [NOTE: Your answers cannot be algebraic epressions.].( pt) The epression equals ( pt) The epression equals A B C where A equals: and B equals: and C equals: 4.( pt) The epression t 4 t 4 6t 5 equals At Bt C where A equals: and B equals: and C equals: 5.( pt) The epression 6 y 6 y equals A By where A equals: and B equals: 6.( pt) The epression 4 4 equals A B C where A equals: and B equals: and C equals: 7.( pt) The epression equals A B C D where A equals: and B equals: and C equals: and D equals: 8.( pt) Factor the polynomial 9 8. Your answer can be written as A B where A B and A equals: and B equals: 9.( pt) Factor the polynomial 6 5. Your answer can be written as A B where A B and A equals: and B equals: 0.( pt) Factor the polynomial 5 6. Your answer can be written as A B where A B and A equals: and B equals:.( pt) Factor the polynomial 0. Your answer can be written as 5 B C D with B, C, and D- integers where B equals: and C equals: and D equals:.( pt) Factor the polynomial 4. Your answer can be written as A B where A B and A equals: and B equals:.( pt) Factor the polynomial t 7 4t 6 5t 5. Your answer can be written as t N t A t B where A B. N equals: and A equals: and B equals: 4.( pt) Factor the polynomial 7. Your answer can be written as A B C where A equals: and B equals: and C equals:

4 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Algebra4Fractions due /7/05 at :00 AM..( pt) Match the epressions below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit A. 5 B. 5 C. 7.( pt) Match the epressions below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit A. 9 B. C. 9.( pt) Match the epressions below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit A. 4 B. 4 C. 4 D. 4 4.( pt) Match the epressions below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit A. 7 B. C. 9 5.( pt) Match the epressions below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit A. 9 B. 9 C ( pt) Match the epressions below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit... b b a b b a b a a b b a a. b b a a b b A. b a a B. a C. ba 7.( pt) Match the epressions below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit. s h s. h s h s. h A. s h s B. s h s 8.( pt) Enter a T or an F in each answer space below to indicate whether the corresponding equation is true or false. An equation is true ony if it is true for all values of the variables. Disregard values that make denominators 0. You must get all of the answers correct to receive credit c 9 c a 7 a y 7 y 9.( pt) Enter a T or an F in each answer space below to indicate whether the corresponding equation is true or false. An equation is true ony if it is true for all values of the variables. Disregard values that make denominators 0. You must get all of the answers correct to receive credit..

5 .. 58 a 58a b 58b

6 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Algebra5Equations due /8/05 at :00 AM. t.( pt) Solve the equation ( pt) Solve the equation for 7 5.( pt) Solve the equation for t t 9 t 7 8 t 0 4.( pt) By completing the square, the epression 0 4 equals A B where A is: and B is: 5.( pt) By completing the square, the epression 8 equals A B where A is: and B is: 6.( pt) The equation 4 0 has two solutions A and B where A B and A is: and B is: 7.( pt) The equation has two solutions A and B where A B and A is: 4 and B is: 8.( pt) The real solution of the equation 5 is: 9.( pt) The equation has two real solutions A and B where A B and A is: and B is: 0.( pt) The equation has three real solutions A, B, and C where A B C and A is: and B is: and C is:.( pt) Now for some review problems: Find the domain of this function: (which reads the 4th root of 4 6 ). The function is defined on the interval from to. Use INF for infinity or -INF for minus infinity. Similar problems in the book: section./-6 Now find the domain of this function: (which reads the 5th root of 4 6 ). The function is defined on the interval from to.

7 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Algebra6WordProblems due /9/05 at :00 AM..( pt) The difference of two positive numbers is 4 and the sum of their squares is 6. Find the numbers. The bigger number is, and the smaller number is..( pt) The area of a rectangle is 0, and its diagonal is 0. Find its dimensions and perimeter. Longer side: Shorter side: Perimeter:.( pt) The length of a rectangular garden is 9 feet longer than its width. If the garden s perimeter is 86 feet, what is the area of the garden in square feet? 4.( pt) A student has scores of 57.75, 59, and 6.5 on his first three tests. He needs an average of at least 60 to earn a grade of D. What is the minimum score that the student needs on the fourth test to ensure a D? Note: The answer need not be an integer. 5.( pt) A cash register contains only five dollar and ten dollar bills. It contains twice as many five s as ten s and the total amount of money in the cash register is 660 dollars. How many ten s are in the cash register? 6.( pt) At :00 PM a man 46 cm tall casts a shadow 5 cm long. At the same time, a tall building nearby casts a shadow 65 m long. How tall is the building? Give your answer in meters. (You may need the fact that 00 cm = m.) 7.( pt) A factory is to be built on a lot measuring 00 ft by 400 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of the lawn be? If the dimensions of the factory are A ft by B ft with A B, then A and B 8.( pt) After robbing a bank in Dodge City, a robber gallops off at mi/h. 0 minutes later, the marshall leaves to pursue the robber at 5 mi/h. How long (in hours) does it take the marshall to catch up to the robber? 9.( pt) Two cyclists, 6 miles apart, start riding toward each other at the same time. One cycles times as fast as the other. If they meet hours later, what is the speed (in mi/h) of the faster cyclist? 0.( pt) ( points) What quantity of 60 per cent acid solution must be mied with a 5 solution to produce 504 ml of a 50 per cent solution?.( pt) The radiator in a car is filled with a solution of 65 per cent antifreeze and 5 per cent water. The manufacturer of the antifreeze suggests that for summer driving, optimal cooling of the engine is obtained with only 50 per cent antifreeze. If the capacity of the raditor is.8 liters, how much coolant (in liters) must be drained and replaced with pure water to reduce the antifreeze concentration to 50 per cent?.( pt) A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is ft. give the area A of the window in square feet when the width is 0.00 ft. Give the answer to two decimal places..( pt) A Norman window has the shape of a rectangle surmounted by a semicircle. The perimeter is.000 ft. Order the widths listed below according to the area of the corresponding Norman window from the lowest area () to highest area (5). You will need to enter the numbers through 5 in the entry blanks below.. Width = 4.00 ft.. Width = 0.00 ft.. Width = ft. 4. Width =.700 ft. 5. Width =.900 ft. Remark: To be able to order the sizes of the windows you are going to have to calculate the area for all five windows from knowing their widths. Since there are several calculations it will save time to figure out and simplify a formula which calculates the area from the width and the perimeter. This is in contrast to the previous problem where, with only one calculation to make, it wasn t necessarily worth the effort to find a general formula. You can use that eample to check your formula however. I do this very frequently when I am doing research and solving problems. Work out a special case first. THEN work out a formula for the general case and use the solution to the special case to check the formula.

8 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Algebra7Inequalities due /0/05 at :00 AM..( pt) The inequality means that is greater than A where A is.( pt) The inequality 0 4 means that is in the closed interval A B where A is: and B is:.( pt) Solve the inequality The solution is is in the open interval A B where A is: and B is: 4.( pt) You arrive in Paris and the forcast is for a low of 6 and a high of degrees Celsius. What is the forcasted low temperature in Fahrenheit? What is the forcasted high temperature in Fahrenheit? 5.( pt) Your friend from Paris arrives in New York and the forcast is for a low of 5 and a high of 8 degrees Fahrenheit. What is the forcasted low temperature in Celsius? What is the focasted high temperature in Celsius? 6.( pt) Consider the inequality 8 The solution of this inequality consists one or more of the following intervals: A and A Find A For each interval, answer YES or NO to whether the interval is included in the solution. A A 7.( pt) Consider the inequality 0 The solution of this inequality consists one or more of the following intervals: A, A B, and B where A B. Find A Find B For each interval, answer YES or NO to whether the interval is included in the solution. A A B B 8.( pt) Consider the inequality The solution of this inequality consists one or more of the following intervals: A B C. Find A Find B Find C A, A B, B C,and C where For each interval, answer YES or NO to whether the interval is included in the solution. A A B B C C 9.( pt) Consider the inequality 7 The solution of this inequality consists one or more of the following intervals: A, A B,and B where A B. Find A Find B For each interval, answer YES or NO to whether the interval is included in the solution. A A B B 0.( pt) Consider the inequality 7 4 The solution of this inequality consists one or more of the following intervals: A B C. Find A Find B Find C A, A B, B C,and C where For each interval, answer YES or NO to whether the interval is included in the solution. A A B B C C

9 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Algebra8AbsoluteValue due //05 at :00 AM..( pt) Evaluate the epression 88..( pt) Evaluate the epression 6..( pt) Evaluate the epression ( pt) Evaluate the epression Give you answer in decimal notation correct to three decimal places or give your answer as a fraction. [NOTE: Your answer can be an algebraic epression. Make sure to include all necessary (, ). ] 5.( pt) Find the distance betweem 8 and 04. [NOTE: Your answer can be an algebraic epression] 6.( pt) Match the statements defined below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit A. B. C. D. E. 7.( pt) To say that 7 4 is the same as saying is in the closed interval A B where A is: and where B is: 8.( pt) To say that 5 is the same as saying is in the closed interval A B where A is: and where B is: 5 9.( pt) To say that 5 7 is the same as saying is in the closed interval A B where A is: and where B is: 5 0.( pt) To say that 7 is the same as saying is in the closed interval A B where A is: and where B is:

10 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Algebra9Systems due //05 at :00 AM..( pt) Solve the system 4 y 4 4 y 5 y.( pt) Solve the system y ln y 5 log y 4log

11 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment GeometryPoints due /0/05 at :00 AM..( pt) Consider the two points and 7 0. The distance between them is: The co-ordinate of the midpoint of the line segment that joins them is: The y co-ordinate of the midpoint of the line segment that joins them is:.( pt) Consider the two points 5 and 8. The distance between them is: The co-ordinate of the midpoint of the line segment that joins them is: The y co-ordinate of the midpoint of the line segment that joins them is:.( pt) Consider the two points and. The distance between them is: The co-ordinate of the midpoint of the line segment that joins them is: The y co-ordinate of the midpoint of the line segment that joins them is: 4.( pt) Consider the two points 5 and 7 9. The distance between them is: The co-ordinate of the midpoint of the line segment that joins them is: The y co-ordinate of the midpoint of the line segment that joins them is: 5.( pt) Find the distance between (, 6) and (-6, 0). 6.( pt) Find the perimeter of the triangle with the vertices at (, ), (-4, 5), and (-, -6). 4 7.( pt) Find the perimeter of the triangle with the vertices at, 6, and ( pt) Find the point 0 b on the y-ais that is equidistant from the points and 5 4. b

12 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment GeometryLines due //05 at :00 AM..( pt) Find the slope of the line through (, -) and (-4, 7)..( pt) A line through (, ) with a slope of has a y-intercept at.( pt) An equation of a line through (, ) which is parallel to the line y has slope: and y intercept at: 4.( pt) An equation of a line through (-, ) which is perpendicular to the line y has slope: and y intercept at: 5.( pt) The equation of the line with slope that goes through the point 6 6 can be written in the form y m b where m is: and where b is: 6.( pt) The equation of the line with slope 4 that goes through the point 6 5 can be written in the form y m b where m is: and where b is: 7.( pt) The equation of the line with slope 5 that goes through the point can be written in the form y m b where m is: and where b is: 8.( pt) The equation of the line with slope that goes through the point 6 where m is: and where b is: 6 can be written in the form y m b 9.( pt) The equation of the line that goes through the points 4 5 and 8 can be written in the form y m b where m is: and where b is: 0.( pt) The equation of the line that goes through the points 4 5 and 9 can be written in the form y m b where m is: and where b is:.( pt) The equation of the line that goes through the points 5 4 and 4 can be written in the form y m b where m is: and where b is:.( pt) The equation of the line that goes through the point 0 9 and is parallel to the -ais can be written in the form y m b where m is: and where b is:.( pt) The equation of the line that goes through the point 5 0 and is parallel to the line y can be written in the form y m b where m is: and where b is: 4.( pt) The equation of the line that goes through the point 4 4 and is perpendicular to the line y 4 can be written in the form y m b where m is: and where b is: 5.( pt) The equation of the line that goes through the point 6 and is perpendicular to the line 4y can be written in the form y m b where m is: and where b is: 6.( pt) The equation of the line that goes through the point 9 4 and is parallel to the line 5 5y can be written in the form y m b where m is: and where b is:

13 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment GeometryConics due //05 at :00 AM..( pt) Match each graph to its equation. (For all graphs on this page, if you are having a hard time seeing the picture clearly, click on it. It will epand to a larger picture on its own page so that you can inspect it more closely.) A. B. y C. y E. y y D. y F. y

14 .( pt) Find an equation of the parabola that has a focus at 6 and a verte at 9 : y Find an equation of its directri: y.( pt) Find the verte, focus, and directri for the following functions. (a) y 4 8 verte : (, ) focus : (, ) directri = (b) y 6y 0 8 verte : (, ) focus : (, ) directri = (c) 6 0 y verte : (, ) focus : (, ) directri y = (d) 8 4y 4 verte : (, ) focus : (, ) directri y = 4.( pt) Write equations for each parabola (If you have a hard time seeing the picture clearly, click on the picture so that you can inspect it more closely.) (a) where K = where H = where A = y K A y 5.( pt) Match each graph to its equation. (For all graphs on this page, if you are having a hard time seeing the picture clearly, click on it. It will epand to a larger picture on its own page so that you can inspect it more closely.) H where K = where H = where A = (b) y K A H.

15 A. y 6 B. 4 y 6 C. 4 y 6 D. 4 y E. 6 y F. y 4 6.( pt) Find the center, vertices, and foci of each ellipse. (a) y 49 5 Center: (, ) Right verte: (, ) Left verte: (, ) Top verte: (, ) Bottom verte: (, ) Right focus: (, ) Left focus: (, ) y (b) 6 8 Center: (, ) Right verte: (, ) Left verte: (, )

16 Top verte: (, ) Bottom verte: (, ) Top focus: (, ) Bottom focus: (, ) (c) 9 6y 6 4y 69 0 Center: (, ) Right verte: (, ) Left verte: (, ) Top verte: (, ) Bottom verte: (, ) Right focus: (, ) Left focus: (, ) 7.( pt) The equation of the ellipse that has a center at 0 6, a focus at 6, and a verte at 5 6, is C A y D B where A B C D y A B C D 8.( pt) Write equations for each ellipse (If you have a hard time seeing the picture clearly, click on the picture so that you can inspect it more closely.) (a) where A = where B = where C = where D = 9.( pt) Match each graph to its equation. (For all graphs on this page, if you are having a hard time seeing the picture clearly, click on it. It will epand to a larger picture on its own page so that you can inspect it more closely.) where A = where B = where C = where D = (b) y A B C D 4.

17 A. y 4 B. 4 C. D. y 4 y 4 y 6 6 E. 4y F. 4 y 0.( pt) The equation of the hyperbola that has a center at 0, is 0, a focus at 0, and a verte at 4. 5 where A B C D C A y D B.( pt) Write equations for each hyperbola (If you have a hard time seeing the picture clearly, click on the picture so that you can inspect it more closely.) (a)

18 where A = where B = where C = where D = (b) A B y C D y A B C D where A = where B = where C = where D =.( pt) Solve the system by graphing each equation and finding the point of intersection. y y 6 y 4 6

19 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Geometry4SubsetsOfR due //05 at :00 AM..( pt) For each graph, determine its system of linear inequalities... A. B. C. D. E. y y y y y y y y y F. None of the above A. B. C. D. E. y 0 y 5 y y 5y y 5y y 5y F. None of the above.( pt) Graph the system: 0 y 0 y 0 0 y 40 List the vertices of the region clockwise starting with (0,0): (0,0); (, ); (, ); (, )..( pt) Graph the system: 6 y 7 0y 8 y 7 List the vertices of the region clockwise starting with the verte whose y-coordinate is the lowest: (, ); (, ); (, ); (, ); (, ). 4.( pt) Choose inequalities that form a system whose graph is the shaded region shown above. A. 7 5y 8

20 B. y C. D. y E. 7 y F. 7 5y 8 G. y H. 7 y 5.( pt) Maimize z 7 y subject to 5 y 5 0 9y 5 4 0y 70 Answer: 6.( pt) Minimize f y 5y subject to 4 6y 6 5 6y 44 Answer:

21 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment SetTheory due /5/05 at :00 AM..( pt) (a) B 4 If n A 9 n B 9 and n A then n A B = (b) If n A B 9 n A B 5 and n A n B then n A =.( pt) Let A , B , C List the elements of the following sets in the increasing order: A B,, A B,,,,, B C A,,, B C A,,,,.( pt) Let U Universal set , A , and B List the elemetns of the following sets in the increasing order: A,,, A B,, A B A B,, 4.( pt) There are a total of foreign language students in a high school where they offer Spanish, French, and German. There are students who take at least languages at once. If there are 40 Spanish students, 50 French students, and 45 German students, how many students take all three languages at once? Answer:

22 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment FunctionsFunctionsGraphs due //05 at :00 AM..( pt) Let f 5. Find f.( pt) Let f 4 and let g h f h f h. Determine each of the following: (a) g (b) g 0 (c) g 0 0 You will notice that the values that you entered are getting closer and closer to a number L. This number is called the limit of g(h) as h approaches 0 and is also called the derivative of f() at the point when =. We will see more of this when we get to the calculus tetbook. Enter the value of L:.( pt) Let f 5 4 and let q h f h f h. Find q ( pt) The domain of the function f 6 is all real numbers ecept for where equals 5.( pt) The domain of the function f 7 consists of one or more of the following intervals: A and A. Find A For each interval, answer YES or NO to whether the interval is included in the solution. A A 6.( pt) The domain of the function f 4 8 is all real numbers in the interval A where A equals 7.( pt) The domain of the function f 9 8 consists of one or more of the following intervals: A, A B and B where A B. Find A Find B For each interval, answer YES or NO to whether the interval is included in the solution. A A B B 8.( pt) The domain of the function f 8 is the closed interval A B where A equals and where B equals 9.( pt) The domain of the function f 5 4 is the closed interval A B where A equals and where B equals 0.( pt) For each of the following functions, decide whether it is even, odd, or neither. Enter E for an EVEN function, O for. an ODD function and N for a function which is NEITHER even nor odd. NOTE: You will only have four attempts to get this problem right!. f 8 6. f 6. f 5 4. f ( pt) Let f and g 5. f g.( pt) Let f 5 5 and g 5. After simplifying, f g.( pt) Let f and g 5. f g 4 4.( pt) Let f 4 and g. After simplifying, f g 5.( pt) The simplest functions are the linear (or affine) functions the functions whose graphs are a straight line. They are important because many functions (the so-called differentiable functions) locally look like straight lines. ( locally means that if we zoom in and look at the function at very powerful magnification it will look like a straight line.) Enter the letter of the graph of the function which corresponds to each statement.. The graph of the line is increasing. The graph of the line is decreasing. The graph of the line is constant 4. The graph of the line is not the graph of a function A B C D 6.( pt) Enter the letter of the graph of the function which corresponds to each statement.. The graph of the line is constant. The graph of the line is not the graph of a function. The graph of the line is increasing 4. The graph of the line is decreasing

23 A B C D 7.( pt) Almost any kind of quantitative data can be represented by a graph and most of these graphs represent functions. This is why functions and graphs are the objects analyzed by calculus. The net two problems illustrate data which can be represented by a graph. Match the following descriptions with their graphs below:. The graph of the distance traveled by a car as it enters a superhighway vs. time.. The graph of the velocity of a car entering a superhighway vs. time.. The graph of the velocity of a car as it drives along a city street vs. time. 4. The graph of the distance traveled by a car as it drives along a city street vs. time. A B C D 8.( pt) Match the following descriptions with their graphs below:. The graph of the number of days until net Friday vs. time.. The graph of the amount of time until midnight net Friday as a function of time.. The graph of the number of days to the nearest Friday (in the future or in the past) as a function of time. 4. The graph of the amount of time to the nearest Friday at midnight vs. time. A B C D 9.( pt) The following questions concern the profits of firm N. The graph

24 of the profits vs. time is given above. For each of the intervals enter the letters corresponding to the descriptions which describe the behavior of the graph on that interval. (The letters in each answer must be in alphabetical order with no spaces between the letters.). The interval from a to b. The interval from b to c. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The firm makes a profit on this interval. B. The firm registers a loss on this interval. C. The profit of the firm increases on this interval. D. The profit of the firm decreases on this interval. E. Assuming the profits are reinvested in the firm the networth of the company is increasing on this interval. F. Assuming the profits are reinvested in the firm the networth of the company is decreasing on this interval. 0.( pt) The function to the left represents the velocity of a race car as it travels a linear track. Negative velocities mean the car is backing up. For each interval, enter all letters whose corresponding statements are true for that interval.. The interval from a to b. The interval from b to c. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The car is moving forward on this interval B. The car is backing up on this interval. C. The forward velocity of the car is increasing on this interval. D. The forward velocity of the car is decreasing on this interval. E. The distance from the starting point is increasing on this interval. F. The distance from the starting point is decreasing on this interval..( pt) The function to the left represents the displacement of a toy race car as it travels a linear track. Negative numbers mean the car is behind the starting line, positive numbers mean it is in front. Postive velocities mean it is moving forward, while negative velocities mean it is moving backwards. Remember that a value which changes from - to - to 0 is increasing! For each interval, enter all letters whose corresponding statements are true for that interval.. The interval from a to b. The interval from b to c. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The car is in front of the starting line on this interval B. The car is behind the starting line on this inteval. C. The velocity of the car is positive on this interval. D. The velocity of the car is negative on this interval. E. The displacement of the car from the starting line is increasing on this interval. F. The displacement of the car from the starting line is decreasing on this interval..( pt) A 5 gram weight is suspended from a string net to a ruler held vertically. The string is jiggled up and down and the graph

25 of the POSITION of the weight vs. time in seconds is given above. The ruler is calibrated in inches and 0 is in the center of the ruler. Enter the letters for the intervals which correspond to the statements below.. The interval from a to b. The interval from b to c. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The weight is moving upward on this interval. B. The weight is moving downward on this interval. C. The upward velocity of the weight is increasing on this interval. D. The upward velocity of the weight is decreasing on this interval. E. The (signed) distance from the starting point is increasing on this interval. F. The (signed) distance from the starting point is decreasing on this interval..( pt) The graph indicates the RATE of absorbtion of carbon dioide into a body of water. The rate varies with time. Positive quantities mean that the carbon dioide is being abosrbed into solution, while negative quantities mean the carbon dioide is being released to the air. For each interval, enter all letters whose corresponding statements are true for that interval.). The interval from a to b. The interval from b to c. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. Carbon dioide is being absorbed by the water on this interval. B. Carbon dioide is being released from the water on this interval. C. The rate at which the carbon dioide is being absorbed is increasing on this interval. D. The rate at which the carbon dioide is being absorbed is decreasing on this interval. E. The total amount of carbon dioide in the water is increasing on this interval. F. The total amount of carbon dioide in the water is decreasing on this interval. 4 4.( pt)

26 Answer the questions about the function whose graph is shown above. Enter the letters for the intervals which correspond to the statements below. The letters for each entry should be in alphabetical order with no spaces.. The interval from a to b. The interval from b to c. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The function is increasing on this interval. B. The function is decreasing on this interval. C. The slope of the function is increasing on this interval. D. The slope of the function is decreasing on this interval. E. The total (signed) area between the graph of the function and the ais is increasing on this interval. F. The total (signed) area between the graph of the function and the ais is decreasing on this interval. G. The shape of the original function is concave up on this interval. H. The shape of the original function is concave down on this interval. 6.( pt) Determine which of the following statements are true and which are false. Enter the T or F in front of each statement. Remember that is the same as and means.. The function f with domain has at least one input which produces a smallest output value.. The function sin on the domain π π has at least one input which produces a smallest output value.. The function sin on the domain π π has at least one input which produces a smallest output value. 4. The function f with domain has at least one input which produces a largest output value. 5. The function f with domain has at least one input which produces a smallest output value. 5.( pt) The graph shown is the graph of the SLOPE of the tangent line of the original function. (This slope is also called the derivative of f.) For each interval, enter all letters whose corresponding statements are true for that interval.. The interval from a to b. The interval from b to c. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The slope of the original function is positive on this interval B. The slope of the original function is negative on this interval. C. The slope of the original function is increasing on this interval. D. The slope of the original function is decreasing on this interval. E. The original function is increasing on this interval. F. The original function is decreasing on this interval. 5 7.( pt) Determine which of the following statements are true and which are false. Enter the T or F in front of each statement. Remember that is the same as and means.. The function f with domain has at least one input which produces a largest output value.. The function sin on the domain π π has at least one input which produces a largest output value.. The function sin on the domain π π has at least one input which produces a largest output value. 4. The function f with domain has at least one input which produces a smallest output value. 5. The function sin on the domain π π has at least one input which produces a smallest output value. 8.( pt) Now for some review problems: Find the domain of this function: 4 4 (which reads the 4th root of 4 ). The function is defined on the interval from to. Use INF for infinity or -INF for minus infinity. Similar problems in the book: section./-6 Now find the domain of this function: 5 4 (which reads the 5th root of 4 ). The function is defined on the interval from to.

27 Given the graphs of f (in blue) and g (in red) to the left answer these questions:. What is the value of f at -5?. For what values of is f g : Separate answers by spaces (e.g 5 7 ). Estimate the solution of the equation g 5 4. On what interval is the function f decreasing? (Separate answers by a space: e.g. - 4 ) 9.( pt) 0.( pt) Let f. Find f f 0 f f f 5 5.( pt) Write the equation describing the graph above: f for in the interval [ to ] for in the interval [ to ] 6.( pt)

28 Match the functions shown in the graph above with their formulas:....( pt) At the surface of the ocean, the water pressure is the same as the air pressure above the water, about 5 lb in, Below the surface the water pressure increases by about 64 lb in for every 0 ft of descent. Write a function f which epresses the water pressure in pounds per square inch as a function of the depth in inches below the ocean surface. f At what depth is the pressure 90 in your answer: lb in? Include the units 4.( pt) Let f 4 and g 8 8. f g is undefined at two points A and B where A B. A is, and B is 5.( pt) Let f and g 9 8. f g is undefined at two points A and B where A B. A is, and B is 6.( pt) Let p Use a calculator or a graphing program to find the slope of the tangent line to the point p when. Give the answer to places. 7.( pt) Use a graphing calculator to find the positive value of which satisfies 0 600cos. Give the answer to decimal places. Remember to calculate the trig functions in radian mode. If you don t have a graphing calculator you can use the program Xfunctions which is installed on most of the Macintoshes in CLARC (ecept for the ones in the Mac classrooms). The program is free and you can download it for your own computer see Mac Software if you have a Mac. If you have a PC try the CD that came with the tetbook see if that will graph equations for you. 8.( pt) Use a graphing calculator to find the largest value of which satisfies Give the answer to decimal places. Remember to calculate the trig functions in radian mode. 9.( pt) The altitude of a right triangle is 8 cm. Let h be the length of the hypotenuse and let p be the perimeter of the triangle. Epress h as a function of p. h p 7

29 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment FunctionsComposition due //05 at :00 AM..( pt) Let f be the linear function (in blue) and let g be the parabolic function (in red) below. If you are having a hard time seeing the picture clearly, click on the picture. It will epand to a larger picture on its own page so that you can inspect it more closely. Note: If the answer does not eist, enter DNE :. (f o g)( ) =. (g o f)( ) =. (f o f)( ) = 4. (g o g)( ) = 5. (f + g)( 4 ) = 6. (f / g)( ) =.( pt) This problem tests calculating new functions from old ones: From the table below calculate the quantities asked for: f g f 4 g 4 5 f g 4 f g 4 Tip: Sometimes webwork will do arithmetic for you. For eample you can type in 4* instead of 44 and webwork will do the calculation for you. This works with many numerical problems, although not all of them. This problem tests calculating new functions from old ones: From the table below calculate the quantities asked for: f g ( pt) f f 4 f g f g 4 Tip: Sometimes WeBWorK will do arithmetic for you. For eample, you can type in 4* instead of 44, and WeBWorK will do the calculation for you. This works with many numerical problems, although not all of them.

30 4.( pt) Let f 5 4 and g 4 4. f g 5.( pt) Let f 4 5 and g 4. After simplifying, f g 6.( pt) Let f 4 and g 4. Match the statements defined below with the letters labeling their equivalent epressions. You must get all of the answers correct to receive credit.. f f. f g. g f 4. g g A. 6 5 B C. 8 6 D ( pt) This problem gives you some practice identifying how more complicated functions can be built from simpler functions. Let f and let g. Match the functions defined below with the letters labeling their equivalent epressions.. g. f g. f 4. g f A. B. C. 6 D. 4 8.( pt) Let f 5, g, and h 0 8. Then f g h 4

31 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment FunctionsTransforms due //05 at :00 AM..( pt) Relative to the graph of y the graphs of the following equations have been changed in what way?. y 6. y. y 4. y 6 A. shifted units down B. stretched horizontally by the factor 6 C. compressed horizontally by the factor 6 D. shifted units right.( pt) Relative to the graph of y the graphs of the following equations have been changed in what way?. y. y. y 4. y A. compressed vertically by the factor B. shifted units down C. shifted units left D. shifted units up.( pt) Relative to the graph of y sin the graphs of the following equations have been changed in what way?. y sin 8. y sin 8. y sin 4. y 8sin 8 A. shifted 8 units down B. stretched horizontally by the factor 8 C. stretched vertically by the factor 8 D. shifted 8 units right Enter the letter of the graph below which corresponds to the transformation of the function.. F. F. F 4. 5F A B C D 5.( pt) Let g be the function below. For all graphs on this page, if you are having a hard time seeing the picture clearly, click on it. It will epand to a larger picture on its own page so that you can inspect it more closely. The domain of g is of the form a b, where a is and b is. and d The range of g is of the form c d, where c is is. Enter the letter of the graph which corresponds to each new function defined below:. g is.. g is.. g is. 4. g is. 4.( pt) This is a graph of the function F : (Click on image for a larger view ) A B C D E F G H

32

33 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Functions4Inverse due /4/05 at :00 AM..( pt) Enter T or F depending on whether the function is one-to-one or not. (You must enter T or F True and False will not work.). d 4. b 4. e c 6 5. a ( pt) Enter a Y (for Yes) or an N (for No) in each answer space below to indicate whether the corresponding function is one-to-one or not. You must get all of the answers correct to receive credit.. h t t t 0. f t t. g t t 4. k f sin 0 π 6. k t 8 t 6.( pt) Enter a T or an F in each answer space below to indicate whether or not the given function has an inverse. Unless otherwise indicated, assume the domain of the function is as large as possible. You must get all of the answers correct to receive credit on the interval ln. 7 sin 4 cos sin 4 5. ln on the interval 0 4.( pt) If f is one-to-one and f 8 5, then f 5 and f 8. If g is one-to-one and g 4 9, then g 9 and g 4. If h is one-to-one and h 6, then h 6 and h 5.( pt) (a) If f is one-to-one and f 5, then f 5 and f. (b) If g is one-to-one and g 0, then g and g 0. 6.( pt) If f 4 6, then f y f 7.( pt) If f 0, then f 5 8.( pt) Let f 9.( pt) Let f 0.( pt) Let f.( pt) Let f.( pt) Let f 4.( pt) Let f f 4 f 4 f 6 0 f 0 f The domain of f is the interval A B where A 4.( pt) Let f 6 and where B f e 5.( pt) Find the inverse for each of the following functions. f 5 9 f g 8 0 g h 5 0 h j j 6.( pt) 8 f e e f = The domain of f is the open interval a b, where a = and b = 7.( pt) Below is the graph of a function f : (Click on image for a larger view )

34 Graph C The inverse of the function f is (A, B or C): Graph A 8.( pt) Below is the graph of a function f : (Click on image for a larger view ) Graph B

35 Graph A Graph D The inverse of the function f is (A, B, C or D): 9.( pt) Match each function to its inverse. (For all graphs on this page, if you are having a hard time seeing the picture clearly, click on it. It will epand to a larger picture on its own page so that you can inspect it more closely.) Graph B. Graph C.

36 . A. 4. B. 5. C. 4

37 D. E. 5

38 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Trigonometry due //05 at :00 AM..( pt) For each of the following angles, find the degree measure of the angle with the given radian measure: π 6 π 4 π π π.( pt) For each of the followings angles, find the degree measure of the angle with the given radian measure: 7π 6 9π 4π 7π 8π.( pt) For each of the following angles, find the radian measure of the angle with the given degree measure (you can enter π as pi in your answers): ( pt) For each of the followings angles (in radian measure), find the sin of the angle (your answer cannot contain trig functions, it must be an arithmetic epression or number): π 6π 4 π π π π 5.( pt) For each of the followings angles (in radian measure), find the cos of the angle (your answer cannot contain trig functions, it must be an arithmetic epression or number): π 6π 4 π π π π 6.( pt) Convert 6 8π to degrees: Convert 844 to radians: π 7.( pt) Evaluate the following epressions sin π cos π tan π cot π 4 sec 4π csc π 8.( pt) If θ 9π 4, then sin θ equals cos θ equals tan θ equals sec θ equals 9.( pt) If θ π 4, then sin θ equals cos θ equals tan θ equals sec θ equals 0.( pt) If θ 8π, then sin θ equals cos θ equals tan θ equals sec θ equals.( pt) If θ 8π ( θ is measured in radians), then sin θ equals cos θ equals tan θ equals sec θ equals.( pt) If θ π 6, then sin θ equals cos θ equals tan θ equals sec θ equals.( pt) If θ π 6, then sin θ equals cos θ equals tan θ equals sec θ equals 4.( pt) If sin θ, 0 θ π, then cos θ equals tan θ equals sec θ equals 5.( pt) If cos θ 5, 0 θ π, then sin θ equals tan θ equals sec θ equals 4 6.( pt) If tan θ 0, 0 θ π, then sin θ equals cos θ equals sec θ equals 7.( pt) If sec θ 5 7, 0 θ π, then sin θ equals cos θ equals

39 tan θ equals 8.( pt) If sin θ 6 (a) cos θ (b) tan θ (c) sec θ (d) csc θ (e) cot θ, and θ is in quadrant II, then find 9.( pt) 6 If tan θ 4 and sin θ 0, then find (a) sin θ (b) cos θ (c) sec θ (d) csc θ (e) cot θ 0.( pt) For each angle below, determine the quadrant in which the terminal side of the angle is found and find the corresponding reference angle. [NOTE : Enter for quadrant I, for quadrant II, for quadrant III, and 4 for quadrant IV.] [NOTE : You can enter π as pi in your answers.] π (a) θ is found in quadrant and θ 5π (b) θ 4 is found in quadrant and θ 7π (c) θ 6 is found in quadrant and θ (d) θ 6 is found in quadrant and θ.( pt) If cos θ (a) tan θ cot θ (b) csc θ tan θ (c) sin θ cos θ 6 and θ is in quadrant III, then find.( pt) For 0 θ π, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as epressions, e.g. you can enter /5). 9 If cos θ 0 then sin θ sec θ csc θ tan θ cot θ =.( pt) For 0 θ π, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as fractions, e.g. you can enter /5). 7 If sec θ 5 then csc θ = sin θ cos θ tan θ cot θ 4.( pt) For 0 θ π, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as fractions, e.g. you can enter /5). If tan θ 9 0 then cot θ sin θ cos θ sec θ csc θ 5.( pt) Find an angle between 0 and π that is coterminal with the given angle. (Note: You can enter π as pi in your answers.) (a) 7π 5 (b) π (c) 65π (d) π 7

40 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment TrigonometryWaves due //05 at :00 AM..( pt) Let y sin 4π e. What is the amplitude? What is the period? What is the phase shift? [NOTE: If needed, you can enter π as pi in your answers.].( pt) π Let y cos. What is the amplitude? What is the period? What is the phase shift? [NOTE: If needed, you can enter π as pi in your answers.].( pt) Let y 0sin 4. What is the amplitude? What is the period? What is the phase shift? [NOTE: If needed, you can enter π as pi in your answers.]

41 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment TrigonometryWordProblems due //05 at :00 AM..( pt) The angle of elevation to the top of a building is found to be 0 from the ground at a distance of 6000 feet from the base of the building. Find the height of the building..( pt) A plane is flying at an elevation of 0000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 6. Find the distance between the plane and the airport. Find the distance between a point on the ground directly below the plane and the airport..( pt) The captain of a ship at sea sights a lighthouse which is 00 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 4. How far is the ship from the base of the lighthouse? 4.( pt) A hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 8 and 0. How high (in feet) is the ballon? 5.( pt) A hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 5 and 8. How high (in feet) is the ballon? [NOTE: mile = 580 feet] 6.( pt) A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 0. From a point 500 feet closer to the mountain along the plain, they find that the angle of elevation is. How high (in feet) is the mountain? 7.( pt) A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 4. From a point 000 feet closer to the mountain along the plain, they find that the angle of elevation is 6. How high (in feet) is the mountain? 8.( pt) A -ft ladder leans against a building so the the angle between the ground and the ladder is 79. How high does the ladder reach on the building? 9.( pt) A circular arc of length 4 feet subtends a central angle of 5 degrees. Find the radius of the circle in feet. (Note: You can enter π as pi in your answer.) feet 0.( pt) Find the equation of the tangent line to the curve y sin at the point π 6. The equation of this tangent line can be written in the form y m b where m and b.( pt) Find the equation of the tangent line to the curve y 4cos at the point π 4π. The equation of this tangent line can be written in the form y m b where m and b

42 Tom Robbins WW Prob Lib Summer 00 WeBWorK assignment Trigonometry4Inverse due /4/05 at :00 AM..( pt) Evaluate the following epressions. Your answer must be an angle π θ π in radians. sin sin cos cos π π..( pt) Evaluate the following epressions. Your answer must be an angle in radians and in the interval (a) sin (b) sin 0 (c) sin.( pt) Evaluate the following epressions. Your answer must be in radians. (a) tan 0 (b) tan (c) tan 4.( pt) Evaluate the following epressions. sin sin cos cos tan tan 5.( pt) Evaluate the following epressions. (a) sin sin (b) tan tan 6.( pt) Evaluate the following epressions. cos sin tan sin 0 7.( pt) Evaluate the following epressions. sin cos tan cos 8.( pt) Evaluate the following epressions. sin tan cos tan 0 9.( pt) Evaluate the following epressions. sin cos 5 tan sin 0.( pt) Match each of the trigonometric epressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank. A. tan arcsin B. cos arcsin C. sin arcsin D. sin arctan E. cos arctan ( pt) Simplify the epression answer = tan cos 4