MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of an exponential function is given. Match the graph to one of the following functions. 1) 1) A) f(x) = 4-x B) f(x) = 4x C) f(x) = - 4x D) f(x) = - 4-x 2) 2) A) f(x) = 2x - 2 B) f(x) = 2x + 2 C) f(x) = 2x + 2 D) f(x) = 2x Find the domain of the function. 3) f(x) = log1/2(x + 4) 3) A) (-, 4) B) (4, ) C) (-, -4) D) (-4, ) 1

2 Match the function to its graph. 4) y = -tan x 4) C) D) 2

3 5) y = tan x + 2 5) C) D) 3

4 6) y = tan (x + ) 6) C) D) 4

5 7) y = tan x - 2 7) C) D) The graph of a logarithmic function is shown. Select the function which matches the graph. 8) 8) A) f(x) = log 5 (-x) B) f(x) = log 5 x C) f(x) = 1 - log 5 x D) f(x) = - log 5 x 5

6 9) 9) A) f(x) = log 2 (x - 2) B) f(x) = log 2 x C) f(x) = log 2 x + 2 D) f(x) = log 2 (x + 2) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 10) f(x) = 5x3 10) 6

7 C) D) Match the graph to the function listed whose graph most resembles the one given. 11) 11) A) reciprocal function B) square function C) absolute value function D) square root function 12) 12) A) constant function B) absolute value function C) reciprocal function D) linear function 13) 13) A) square root function B) cube root function C) cube function D) square function 7

8 14) 14) A) cube root function B) square root function C) square function D) cube function Graph the circle. 15) x2 + y2 = 16 15) C) D) 8

9 Match the graph to one of the listed functions without using a graphing utility. 16) 16) A) f(x) = x2 + 2x + 1 B) f(x) = x2-2x C) f(x) = x2-2x + 1 D) f(x) = x2 + 2x Use the Factor Theorem to determine whether x - c is a factor of f(x). 17) f(x) = x3 + 3x2-8x + 10; x ) A) Yes B) No Use a graphing utility to solve the equation on the interval 0 x < 360. Express the solution(s) rounded to one decimal place. 18) 3 cos2 x + 2 cos x = 1 18) A) 51.8, B) 103.2, 145.2, 283.2, C) 70.5, 180.0, D) 49.8, 130.2, 229.8, ) 7 cot2 x - 5 = 0 19) A) 70.5, 109.5, B) 51.8, C) 103.2, 145.2, 283.2, D) 49.8, 130.2, 229.8,

10 Solve the problem. 20) Decide which of the rational functions might have the given graph. 20) A) R(x) = C) R(x) = x - 2 (x + 2)(x - 3) x + 2 (x - 2)(x + 3) B) R(x) = D) R(x) = 2 - x (x + 2)(x - 3) x - 2 (x + 2)2(x - 3)2 21) A life insurance company uses the following rate table for annual premiums for women for term life insurance. Use a graphing utility to fit an exponential function to the data. Predict the annual premium for a woman aged 70 years. Age Premium $103 $133 $190 $255 $360 $503 $818 A) y = ln (x), $1723 B) y = 6.367e0.068x, $743 C) y = x4.06, $1233 D) y = 8.94e0.068x, $ ) ) The logistic growth model P(t) = represents the population of a bacterium in e-0.334t a culture tube after t hours. When will the amount of bacteria be 650? A) 6.48 hours B) hours C) 2.64 hours D) 8.63 hours 22) 23) Determine which rational function R(x) has a graph that crosses the x-axis at -1, touches the x-axis at -4, has vertical asymptotes at x = -2 and x = 3, and has one horizontal asymptote at y = -2. A) R(x) = -2(x -3)(x + 2) 2, x -4, -1 B) R(x) = -(x + 1)(x + 4) 2, x 2, -3 (x + 4)2(x +1) 2(x - 2)2(x + 3) C) R(x) = -2(x + 1)(x + 4) (x + 2)(x - 3), x -2, 3 D) R(x) = -2(x + 1)(x + 4) 2, x -2, 3 (x + 2)2(x - 3) 23) 24) If f( ) = sin and f(a) = - 1, find the exact value of f(-a). 24) 6 A) B) C) 5 6 D)

11 25) If f( ) = sec and f(a) = 6, find the exact value of f(-a). 25) A) B) -6 C) 6 D) ) Find an equation of the line with slope undefined and containing the point (-6, 4). 26) A) x = 4 B) y = 4 C) y = -6 D) x = -6 27) The concentration of a drug in the bloodstream, measured in milligrams per liter, can be modeled by the function, C(t) = 12t + 4, where t is the number of minutes after injection of the 3t2 + 2 drug. When will the drug be at its highest concentration? Approximate your answer rounded to two decimal places. A) t = 0.55 minutes after the injection is given B) at the time of injection C) t = 3.65 minutes after the injection is given D) t = 4 minutes after the injection is given 27) 28) Decide which of the rational functions might have the given graph. 28) A) f(x) = x2 B) f(x) = 1 2x C) f(x) = 1 x D) f(x) = 1 x2 11

12 29) Which of the following polynomial functions might have the graph shown in the illustration below? 29) A) f(x) = x2(x - 2)2(x - 1)2 B) f(x) = x(x - 2)(x - 1)2 C) f(x) = x(x - 2)2(x - 1) D) f(x) = x2(x - 2)(x - 1) 30) A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8 per square centimeter, while the sides are made of material that costs 5 per square centimeter. Which function below describes the total cost of the material as a function of the radius r of the cylinder? A) C(r) = 0.16 r r C) C(r) = 0.08 r r B) C(r) = 0.08 r r D) C(r) = 0.16 r r 30) For the given functions f and g, find the requested composite function value. 31) Given f(x) = x - 6 and g(x) = x2 + 9, find (g f)(-2). 31) x A) 25 B) 13 C) D) 7 13 Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 32) cos (-60 ) 32) A) 3 2 B) C) 1 2 D) Graph the function. 12

13 33) f(x) = 0.3x 33) C) D) 13

14 34) y = 1 x 34) C) D) 14

15 35) f(x) = -x + 2 x < 0 x + 3 x 0 35) C) D) 15

16 36) f(x) = x + 1 if x < 1-3 if x 1 36) C) D) State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 37) f(x) = -10x3-7x2-9 37) A) No; the last term has no variable B) Yes; degree 6 C) Yes; degree 5 D) Yes; degree 3 16

17 Find the exact value of the expression. 38) cos ) A) 4 B) - 4 C) 3 4 D) -3 4 Find the exact value of the expression. Do not use a calculator. 39) tan -1 tan ) A) 8 B) 8 C) -8 D) - 8 The graph of a function f is given. Use the graph to answer the question. 40) How often does the line y = 4 intersect the graph? 40) A) once B) twice C) three times D) does not intersect Find the vertical asymptotes of the rational function. 41) h(x) = x + 8 x2-16 A) x = 0, x = 16 B) x = 16, x = -8 C) x = -4, x = 4, x = -8 D) x = -4, x = 4 41) Find the midpoint of the line segment joining the points P1 and P2. 42) P1 = (7, 1); P2 = (-16, -16) 42) A) (- 9 2, ) B) (9, 15) C) ( 2 2, 17 ) D) (-9, -15) 2 17

18 Match the correct function to the graph. 43) 43) A) y = x - 1 B) y = x C) y = x - 1 D) y = x ) 44) A) y = -2x2 + 1 B) y = -2x2-1 C) y = 1 - x2 D) y = -2x2 45) 45) A) y = 2 - x B) y = x + 2 C) y = x - 2 D) y = 1 - x 18

19 Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. 46) f(x) = -3x 2 46) 9x3-1 A) symmetry with respect to the y-axis B) symmetry with respect to the origin C) neither Find the value for the function. 47) Find f(2x) when f(x) = 7x2 + 2x. 47) A) 28x2 + 4x B) 14x2 + 8x C) 14x2 + 4x D) 2 7x2 + 2x Use a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places. 48) 2x4-5x2 + 7x = 14 48) A) {-2.32, 1.70} B) {-2.31, 1.70} C) {-2.30, 1.69} D) {-2.31, 1.69} Complete the identity. 49) csc (2 ) + cot (2 ) =? 49) A) cot B) tan C) tan 2 D) cot 2 List the intercepts for the graph of the equation. 50) y = x ) A) (0, -27), (3, 0) B) (0, -3), (-3, 0) C) (0, -3), (0, 3) D) (-27, 0), (0, 3) 19