SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question

Size: px

Start display at page:

Download "SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question"

Lesley Shelton
5 years ago
Views:

1 Midterm Review 0 Precalculu Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question ) A graph of a function g is shown below. Find g(0). (-, ) (-, 0) (0, -) - - ) Find f(k - ) for f() = - - ) Given f() = -[[-.]], find f(.7). Find the domain of the function. ( + )( - ) ) f() = + ) f() = ) f() = - 7 7) Find the domain and range of t() = -. Determine whether the graph is the graph of a function. 8)

2 9) What is the domain and range of the function below? ) Determind the intervals on which the function is increasing, decreasing and constant ) The height in feet of a firework t seconds after it is launched is modeled b h(t) = -t+t+. a. Find its average speed from to seconds. b. When does the firework reach the highest point before falling to the ground? ) The function S() = gives the predicted sales volume of a compan, in millions of items, where is the number of ears from now. Determine the predicted sales ears from now. ) A manufacturing compan estimates that it will have a Profit of $P, in thousands of dollars, if it produces units of its product, where P() = for 0. Then find the relative maimum. How man units should be produced to obtain the maimum profit? What is the maimum profit? ) Elissa wants to set up a rectangular dog run in her backard. She has 0 feet of fencing to work with and wants to use it all. If the dog run is to be feet long, epress the area of the dog run as a function of. ) From a -inch b -inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a bo. Let represent the length of the sides of the squares, in inches, that are cut out. Epress the volume of the bo as a function of. ) Graph f() =, for - -, for <.

3 7) Graph f() = + +, for - + -, for = -. HONORS!!! 8) Graph = -. 9) Graph f() = - if < - + if. 0) Graph f() = if < if 0. ) Find (f - g)() if f() = - and g() = 7 -. ) Find (fg)(-) when f() = + and g() = + -. ) Find (f/g)( ) when f() = - and g() = +. ) For f() = - and g() = +, what is the domain of f+g? ) For f() = - and g() = +, what is the domain of f o g? ) If f() = - and g() = -, find (g f)() and state the domain. 7) What is the domain of f + g? 8) Find the inverse of f() = -. 9) Find the inverse of f() = + - ; and state the domain. 0) Determine if f() = - + ; is one-to-one.

4 Compute and simplif the difference quotient ) f() = ) f() = 9 - f( + h) - f(), h 0. h Determine if the graph is smmetric with respect to -ais, -ais, and origin. ) - - ) ) Determine algebraicall whether the graph is smmetric with respect to the -ais, the -ais, and the origin. ) + = - 7) + =

5 8) = ( - )( + ) 9) Determine if the given function is even, odd or neither. - - Determine algebraicall whether the function is even, odd, or neither even nor odd. 0) f() = + ) f() = -7 ) f() = ) f() = - - ) f() = - ) How can the graph of f() = be obtained from the graph of =? ) How can the graph of f() = ( - ) - be obtained from the graph of =? 7) How can the graph of = - be obtained from the graph of =. 8) Write an equation for a function with the shape of = vv, reflected across the -ais, verticall stretched b a factor of 7 and then shifted unit downward.

6 9) Given f() below, sketch = f( - ) ) Given f() below, graph g() = f() -. ) Given the equation of f() and the graph of g(), write an equation for g(). f() is the parent function. f() = - + (-, ) (, ) g() = (-, ) (, ) (0, 0) (-, -) - (, -) (0, 0) (-, -) - (, -) - -

7 ) From the graph of the function, if - is an element of the range, find the corresponding element of the domain. - - ) For the function f() = - +, with domain of [-, «), find the range. ) Determine the interval on which f() = is increasing and decreasing. ) What is the ais of smmetr and verte of f() = - + -? ) Graph = - ( + ) -. 7) What is the range of f() = - 8 +? 8) The area of a square is numericall less than the perimeter. Find the length of the side, if the side is greater than. 9) At Allied Electronics, production has begun on the X- Computer Chip. The total cost function is given b C() = 7 + and the total profit function is given b P() = , where represents the number of boes of computer chips produced. The total revenue function, R(), is such that R() = C() + P(). Find R(). 0) John owns a hotdog stand. He has found that his profit is represented b the equation P = , with P being profits and the number of hotdogs sold. How man hotdogs must he sell to earn the most profit? ) A rock falls from a tower that is 7 ft high. As it is falling, its height is given b the formula h = 7 - t. How man seconds will it take for the rock to hit the ground (h=0)? Simplif. Write our answers in the form of a+ib, where a and b are real numbers. ) ( + i) - ( - i) ) (8 - -) ( + 0) ) (7 - i) ) + i ( - i) 7

8 ) - 7i +i + - i +i 7) (-i)7 8) Solve - + = 0 and round to the nearest thousandths place. 9) Solve for all comple soltions: + 7 = 8. Don't estimate!!! 70) Solve f() = ) Use a graphing calculator or to graph P() = The label all the etrema. You can approimate!!! 7) Sketch f() = ) Use the Intermediate Value Theorem to find the interval(s) in which the zero(s) occur for P() = on (-, ). 7) According to Descartes' Rule of Signs, how man positive and negative real zeros could f() = have? 7) Determine the smallest upper bound of P() = ) Sketch f() = ) Given f() = is - a factor? 78) Re-write P() = using the division algorithm P() = d() œ Q() + R() if d() = ) Divide using snthetic division. ( ) d ( - ) 80) Use snthetic division to divide is divided b -. Must use the specified method!!! 8) Determine if and are zeros of f() = ) Use snthetic division and the Remainder Theorem to evaluate f(-) for f() = -. You must show work!!! 8) Factor f() = and state the zeros of the polnomial function. 8) Find the zeros of f() = -( - 7)( + ) and list the multiplicit of each. 8) A polnomial function of degree with rational coefficients has i, - + i, - as zeros. Find the other zeros. 8

9 8) Write a polnomial function of degree with - as a zero of multiplicit, 0 as a zero of multiplicit, and as a zero of multiplicit. 87) Write a polnomial function of lowest degree with and -i as zeros. 88) Write a polnomial function of lowest degree with zeros at + i and. 89) Write a polnomial function of lowest degree with zeros at -i and. 90) List all the possible zeros of P() = ) Find all the zeros of f() = , then re-write as a product of linear factors. 9) Find onl the rational zeros of f() = ) Determine whether f() = + 9 is continuous at = -. If discontinuous, identif the tpe of discontinuit + as infinite, jump or removable. 9) Determine whether f() = as infinite, jump or removable. is continuous at = -. If discontinuous, identif the tpe of discontinuit 9) Determine the value of k such that f() = if < +k if is continuous when =. 9) Solve =. 97) Solve t + t + t = 7. HONORS!!! 98) Solve 99) Sketch f() = 0) Sketch f() = ) Sketch f() = ) Sketch f() = + + = HONORS!!! + 9. HONORS!!! - -. HONORS!!!. HONORS!!! + +. HONORS!!! 9

10 ) Sketch f() = - -. HONORS!!! - ) Write a rational function with vertical asmptotes at = - and = 8, a horizontal asmptote at = and an -intercept at (, 0). HONORS!!! ) Write a rational function with an oblique asmptote at = -. HONORS!!! ) The point (-, ) is on a circle that has center (9, -). Find the length of the diameter of the circle. 7) Write the equation of a circle with endpoints of a diameter at (-9, 9) and (, ). 8) Find the focus and directri of - = 0. 9) Find the verte, focus and directri of = 0. ) Graph ( - ) = 8( + ). HINT: You ma need to put the equation in the format ou are used first. ) A tunnel is in the shape of a parabola. The maimum height is m and it is 9 m wide at the base. What is the vertical clearance m from the edge of the tunnel? A = m and B = 9 m ) Find the center and radius of = - +. ) Find the center, vertices and foci of = 0. ) Write the equation of an ellipse with vertices at (-, 0) and (, 0) and a length of minor ais of. ) Write the equation of the hperbola with vertices at (0, ) and (0,- ) and asmptotes at = 9, = - 9. ) Find the center, foci and asmptotes of = 0. 7) Graph ( + ) - ( - ) 9 =.

11 Answer Ke Testname: MIDTERM REVIEW 0.TST ) Answer: - ) Answer: f(k - ) = k - 8k + ) Answer: ) Answer: (-«, «) ) Answer: (-«,- 7 ) U (- 7, ) U (,«) ) Answer: (-«,«) 7) Answer: Domain = { }; Range = { 0} 8) Answer: Yes 9) Answer: Domain: [-p, p ]; Range: [-, ] ) Answer: Increasing on (-, 0); Decreasing on (-, -) and (, ); Constant on (0, ) ) Answer: ft/sec; t=/ sec ) Answer:.9 million ) Answer: 0 units; $,80,000 ) Answer: A() = 0 - ) Answer: V() = ) Answer: ) Answer: - -

12 Answer Ke Testname: MIDTERM REVIEW 0.TST 8) Answer: ) Answer: - 0) Answer: - ) Answer: - + ) Answer: 9 ) Answer: - ) Answer: [-, «) ) Answer: All real numbers - ) Answer: (g f)() = ; (-«, ) U (,«) ) Answer: [-,] 8) Answer: f-() = + 9) Answer: f-() = + - ; 0) Answer: Yes because the domain is restricted. ) Answer: h; h 0 9 ) Answer: (9 - h)(9 - ) ; h 0

13 Answer Ke Testname: MIDTERM REVIEW 0.TST ) Answer: origin ) Answer: -ais ) Answer: -ais ) Answer: -ais onl 7) Answer: -ais onl 8) Answer: -ais onl 9) Answer: Odd 0) Answer: Even ) Answer: Even ) Answer: Odd ) Answer: Odd ) Answer: odd ) Answer: Stretch it horizontall. Scale b a factor of. ) Answer: Shift it units horizontall to the right. Shift it units downward. 7) Answer: Reflect it across the -ais. 8) Answer: f() = - 7vv - 9) Answer: ) Answer: ) Answer: g() = f() ) Answer: - ) Answer: (-«, ] ) Answer: Increasing on (-, «); decreasing on (-«, -)

14 Answer Ke Testname: MIDTERM REVIEW 0.TST ) Answer: = 9 ; 9, 7 ) Answer: ) Answer: [-, «) 8) Answer: units 9) Answer: R() = ) Answer: hotdogs ) Answer:. s ) Answer: - + 9i ) Answer: i ) Answer: - i ) Answer: i ) Answer: 7) Answer: i i 8) Answer: 0.,.87 9) Answer: -,, - 7, 7 70) Answer:, -,, - 7) Answer: Absolute Minimum: (-, -) Relative Minimum: (, ) Relative Maimum: (0, ) Absolute Maimum: None

15 Answer Ke Testname: MIDTERM REVIEW 0.TST 7) Answer: 0 7) Answer: (-, -) and (-, 0) 7) Answer: or 0; or 0 7) Answer: 7) Answer: 0-77) Answer: Yes 78) Answer: P() = ( - + )œ( + - ) + (- + ) 79) Answer: + 80) Answer: ) Answer: No; es 8) Answer: - - 8) Answer: ( + )( + )( + ) ; -, -, - 8) Answer: -, multiplicit ; 0, multiplicit ; 7, multiplicit 8) Answer: -i, - - i, + 8) Answer: f() =

16 Answer Ke Testname: MIDTERM REVIEW 0.TST 87) Answer: f() = ) Answer: f() = ) Answer: f() = ) Answer: ±, ±/, ±, ±, ±/, ±, ±9, ±9/, ±8 9) Answer: -, -i, i; f() = ( + )( + i)( - i) 9) Answer: No rational zeros 9) Answer: discontinuous; infinite 9) Answer: discontinuous; removable 9) Answer: k = 9) Answer: 97) Answer: 98) Answer: 0, - 99) Answer: 0) Answer: No -intercepts, -intercept: 0, ;

17 Answer Ke Testname: MIDTERM REVIEW 0.TST ) Answer: No -intercepts, no -intercepts ; ) Answer: -intercept: (0, 0), -intercept: (0, 0) ; ) Answer: -intercept: -, 0, -intercept: (0, ) ; ) Answer: R() = - - ) Answer: R() = - + ) Answer: 8 7) Answer: ( + ) + ( - ) = 8) Answer: (9, 0); = -9 9) Answer: -,- ; (-, -); = - 7

18 Answer Ke Testname: MIDTERM REVIEW 0.TST ) Answer: ) Answer:.8 m ) Answer: (, -7); r = ) Answer: (,-); (-,-), (,-); (-,-), (,-) ) Answer: + 9 = ) Answer: - = ) Answer: (, ); ( 7, ), (- 7, ); - = ( - ), - = -( - ) 7) Answer: - - 8

Math 121. Practice Questions Chapters 2 and 3 Fall Find the other endpoint of the line segment that has the given endpoint and midpoint.

Math 121. Practice Questions Chapters 2 and 3 Fall Find the other endpoint of the line segment that has the given endpoint and midpoint. Math 11. Practice Questions Chapters and 3 Fall 01 1. Find the other endpoint of the line segment that has the given endpoint and midpoint. Endpoint ( 7, ), Midpoint (, ). Solution: Let (, ) denote the