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1 Practice Eam 2 CH 1 Functions, transformations and graphs Math 3ML FALL 2016 TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Provide reasoning. NO EXPLANATION NO CREDIT. NOTE: THE KEY MAY NOT BE CORRECT. 1) If varies DIRECTLY as 2, then =k, for some variation constant k. 1) 2) If varies jointl as and z and inversel as w, then = k zw. 2) 3) The graph of g()= - can be obtained from the reflecting the graph of f()= about the ais. 4) Stretching the graph of f() verticall b 3 units means graphing the function =f(3). ) Shifting the graph of f() to the right b 3 means graphing the function =f(+3). 3) 4) ) 6) Shifting the graph of f() up b 3 means graphing the function =f(+3). 6) 7) Shifting the graph of = down b 3 means graphing the function = ) 8) Shifting the graph of = left b 3, then flipping about the ais means graphing the function = ) 9) The function f() = - 3 is and odd function and is decreasing on the interval (-, ). 9) ) The function f() = +4 is even. ) 11) The function f()= (-2) 2 has an absolute maimum at = 2. 11) 12) The graph of the monthl average gas price in Honolulu is alwas increasing. 12) 13) The annual average rate of change of a person's height is alwas increasing. 13) 1

2 14) In general, a student's math test score varies directl as the amount of work dedicated. 14) 1) The area of a circle varies directl with the square of the radius of the circle. 1) 16) The variable z varies directl with the sum of the squares of and. When z=2, =3 and =4. Then z = 13 when =12 and =. 16) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 17) In 1980, the population of a cit was 6. million. B 1992 the population had grown to 9.2 million. Find the average rate of change in population from 1980 to ) Determine whether the relation represents a function. If it is a function, state the domain and range. 18) {(-1, -3), (-2, -2), (-2, 0), (2, 2), (14, 4)} 18) 19) {(-1, -6), (2, ), (, -3), (6, -1)} 19) Determine whether the equation defines as a function of. 20) = ± ) Find the value for the function. 21) Find f( + h) when f() = ) Solve the problem. 22) If f() = - 3A and f(9) = -3, what is the value of A? 22) For the given functions f and g, find the requested function and state its domain. 23) f() = 4-4; g() = 3-7 Find f g. 23) 2

3 Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if an, and an smmetr with respect to the -ais, the -ais, or the origin. 24) 24) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a function f is given. Use the graph to answer the question. 2) For what numbers is f() < 0? 2) A) (-, -12) B) (-12, 14) C) (-12, ) D) [-20, -12), (14, 20) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Answer the question about the given function. 26) Given the function f() = 2-4, if = -2, what is f()? What point is on the graph of f? 26) + 3 3

4 Solve the problem. 27) Michael decides to walk to the mall to do some errands. He leaves home, walks 2 blocks in 9 minutes at a constant speed, and realizes that he forgot his wallet at home. So Michael runs back in 6 minutes. At home, it takes him 4 minutes to find his wallet and close the door. Michael walks blocks in 1 minutes and then decides to jog to the mall. It takes him 8 minutes to get to the mall which is 3 blocks awa. Draw a graph of Michael's distance from home (in blocks) as a function of time. 27) Distance time The graph of a function is given. Decide whether it is even, odd, or neither. What function is this? 28) )

5 The graph of a function is given. Determine on what interval is the function increasing, decreasing and constant. 29) (0, 1) 29) The graph of a function f is given. Use the graph to answer the question. 30) 30) (-8, ) (2.2, 3.9) (-, 0) (4, 0) - (-9., 0) (0, 0) (, -2.) (-2., -3.3) - Find the numbers, if an, at which f has a local maimum. What are the local maima? Find the average rate of change for the function between the given values. 31) f() = ; from 1 to 3 31) The graph of a function is given. Decide whether it is even, odd, or neither. 32) )

6 Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 33) f() = 3-33) Graph the function. 34) + 1 if -9 < f() = -7 if = if > 34) Solve the problem. 3) Elissa wants to set up a rectangular dog run in her backard. She has 24 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. 3) 36) Bob wants to fence in a rectangular garden in his ard. He has 86 feet of fencing to work with and wants to use it all. If the garden is to be feet wide, epress the area of the garden as a function of. 36) 6

7 37) Sue wants to put a rectangular garden on her propert using 62 meters of fencing. There is a river that runs through her propert so she decides to increase the size of the garden b using the river as one side of the rectangle. (Fencing is then needed onl on the other three sides.) Let represent the length of the side of the rectangle along the river. Epress the garden's area as a function of. 37) Locate an intercepts of the function. 38) 1 if -9 < -3 f() = if -3 < 9 3 if ) The graph of a piecewise-defined function is given. Write a definition for the function. 39) 39) (-4, 2) (, 0) - - 7

8 Solve the problem. 40) One Internet service provider has the following rate schedule for high-speed Internet service: 40) Monthl service charge $ st 0 hours of use Net 0 hours of use Over hours of use free $0./hour $1.2/hour a. What is the charge for 0 hours of high-speed Internet use in one month? b. What is the charge for 12 hours of high-speed Internet use in one month? c. What is the charge for 1 hours of high-speed Internet use in one month? d. Construct a funtion that gives the monthl charge C for hours of high-speed internet use. Note: the solution in the back ma not be relevant. For the following graphs. A. Eplain in words how ou would get the graph of these functions from the basic function. B. Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 41) f() = )

9 Using transformations, sketch the graph of the requested function. 42) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(), where F() = - f( -2) + 3. The answer ke ma not be accurate. 42) (0, 7) (-3, ) (3, 3) Find the function. 43) Find the function that is finall graphed after the following transformations are applied to the graph of =. The graph is shifted down 7 units, reflected about the -ais, and finall shifted right units. 43) 44) Find the function that is finall graphed after the following transformations are applied to the graph of = 2. The graph is shifted up 4 units, reflected about the -ais, and finall shifted right 8 units. 44) If varies directl as, find a linear function which relates them. 4) = 4 when = 24 4) Find an equation of variation for the given situation. 46) varies inversel as, and = 24 when = 4 46) 9

10 47) varies inversel as the square of, and = 8 when = 2 47) Solve. 48) The amount of water used to take a shower is directl proportional to the amount of time that the shower is in use. A shower lasting 22 minutes requires 17.6 gallons of water. Find the amount of water used in a shower lasting 9 minutes. 48) 49) The amount of paint needed to cover the walls of a room varies jointl as the perimeter of the room and the height of the wall. If a room with a perimeter of 30 feet and 6-foot walls requires 1.8 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 70 feet and -foot walls. 49) 0) Find the average rate of change of the graph between the two points listed. 0)

11 Answer Ke Testname: PRACTICEEXAM2-CH1-FALL16 1) FALSE 2) FALSE 3) FALSE 4) FALSE ) FALSE 6) FALSE 7) FALSE 8) FALSE 9) FALSE ) FALSE 11) FALSE 12) FALSE 13) FALSE 14) FALSE 1) FALSE 16) FALSE 17) 9 40 million per ear (1.3) Solve Apps: Average Rate of Change 18) not a function (1.1) Determine Whether a Relation Represents a Function 19) function domain: {-1, 2,, 6} range: {-6,, -3, -1} (1.1) Determine Whether a Relation Represents a Function 20) not a function (1.1) Determine Whether a Relation Represents a Function 21) h - 3h h - 3 (1.1) Find the Value of a Function 22) A = 86 (1.1) Find the Value of a Function 11

12 Answer Ke Testname: PRACTICEEXAM2-CH1-FALL16 23) (f g)() = ; all real numbers (1.1) Form the Sum, Difference, Product, and Quotient of Two Functions 24) function domain: { -2} range: { 0} intercepts: (-2, 0), (0, 2), (2, 0) smmetr: none (1.2) Identif the Graph of a Function 2) B (1.2) Obtain Information from or about the Graph of a Function 26) 0; (-2, 0) (1.2) Obtain Information from or about the Graph of a Function ) Time (in minutes) (1.2) Obtain Information from or about the Graph of a Function 28) odd (1.3) Determine Even and Odd Functions from a Graph 29) constant (1.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant 30) f has a local maimum at = -8 and 2.2; the local maimum at -8 is ; the local maimum at 2.2 is 3.9 (1.3) Use a Graph to Locate Local Maima and Local Minima 31) -3 (1.3) Find the Average Rate of Change of a Function 32) neither (1.3) Determine Even and Odd Functions from a Graph 33) = 6-6 (1.3) Find the Average Rate of Change of a Function 12

13 Answer Ke Testname: PRACTICEEXAM2-CH1-FALL16 34) (, 6) (, 3) - - (-9, -8) - - (, -7) (1.4) Graph Piecewise-defined Functions 3) A() = 12-2 (1.6) Build and Analze Functions 36) A() = 43-2 (1.6) Build and Analze Functions 37) A() = (1.6) Build and Analze Functions 38) (0, 0) (1.4) Graph Piecewise-defined Functions 39) f() = - 1 if if 0 < 3 (1.4) Graph Piecewise-defined Functions 40) $18.00 $24.2 $6.0 (1.4) Graph Piecewise-defined Functions 41) (1.) Graph Functions Using Vertical and Horizontal Shifts 13

14 Answer Ke Testname: PRACTICEEXAM2-CH1-FALL16 42) (-3, 0) - (-, -3) - (1, -) (1.) Graph Functions Using Vertical and Horizontal Shifts 43) = (1.) Graph Functions Using Reflections about the -Ais and the -Ais 44) = (1.) Graph Functions Using Reflections about the -Ais and the -Ais 4) f() = 6 (1.7) Construct a Model Using Direct Variation 46) = 96 (2.) Find Equation: Inverse Variation ( = k/) 47) = 32 2 (2.) Find Equation: Combined Variation I 48) 7.2 gallons (1.7) Construct a Model Using Direct Variation 49) 7 quarts (1.7) Construct a Model Using Joint or Combined Variation 0) 14

Math 1050 REVIEW for Exam 1. Use synthetic division to find the quotient and the remainder. 1) x3 - x2 + 6 is divided by x + 2

Math 1050 REVIEW for Exam 1. Use synthetic division to find the quotient and the remainder. 1) x3 - x2 + 6 is divided by x + 2 Math 0 REVIEW for Eam 1 Use snthetic division to find the quotient and the remainder. 1) 3-2 + 6 is divided b + 2 Use snthetic division to determine whether - c is a factor of the given polnomial. 2) 3-32