Assignment 5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Assignment 5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given functions f and g, find the requested composite function. 1) f(x) = 4x2 + 2x + 5, g(x) = 2x - 6; Find (g f)(x). 1) A) 8x2+ 4x + 16 B) 4x2 + 4x + 4 C) 8x2 + 4x + 4 D) 4x2 + 2x - 1 2) f(x) = -2x + 7, g(x) = x + 5; Find (g f)(x). 2) A) -6x + 26 B) -6x + 17 C) -6x - 16 D) 6x + 26 For the given functions f and g, find the requested composite function value. ) f(x) = 9x2-4x, g(x) = 8x - 10; Find (f g)(10). ) A) 6,950 B) 60,200 C) 4,820 D) 6870 Evaluate the expression using the values given in the table. 4) (g f)(1) 4) x f(x) x g(x) A) 6 B) -8 C) -4 D) 10 5) 5) f(g(-5)) A) -2 B) 0 C) 1 D) -5 1

2 Determine whether the function is one-to-one. 6) 6) Domain Range $ years 5 years $15,000 A) One-to-one B) Not one-to-one Decide whether or not the functions are inverses of each other. 7) f(x) = 4x - 2, g(x) = x ) A) Yes B) No Determine whether the function is one-to-one. 8) 8) Domain Range 5 years $ years $8000 $12,000 A) One-to-one B) Not one-to-one Decide whether or not the functions are inverses of each other. 9) f(x) = 1 + x x, g(x) = 1 x - 1 9) A) Yes B) No Find the inverse of the function and state its domain and range. 10) 10) Time at Job Bonus $ years $14,000 A) Bonus $2000 $14,000 D: {2000, 14,000} R: {10, 0} Time at Job 0 years 2

3 B) Bonus $2000 $14,000 Time at Job 0 years C) D) D: {10, 15, 20, 0} R: , 7000, 14,000} Bonus $2000 $14,000 D: {2000, 6000, 7000, 14,000} R: {10, 15, 20, 0} Bonus $2000 $14,000 D: {2000} R: {10} Time at Job 0 years Time at Job 0 years Graph the function. 11) f(x) = 5ex 11)

4 A) B) C) D) Solve the equation. 12) 27x = 81 12) A) B) C) D) 4 4 Approximate the value using a calculator. Express answer rounded to three decimal places. 1) e 1) A) B) C) D) Solve the equation. 14) 24x = 1 14) 1 A) {1} B) C) {0} D) 24 15) 4(5-2x) = 4 15) A) {} B) {1} C) {2} D) {-2} 4

5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 16) A rumor is spread at an elementary school with 1200 students according to the model 16) N = 1200(1 - e-0.16d) where N is the number of students who have heard the rumor and d is the number of days that have elapsed since the rumor began. How many students will have heard the rumor after 5 days? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function. 17) f(x) = 1 x 4 17) A) B) C) D) 5

6 Solve the equation. 18) 2x2 - = 64 18) A) { 5, - 5} B) {6} C) {} D) {, -} Solve the problem. 19) Suppose that f(x) = 4x + 2. If f(x) = 258, what is x? 19) A) -4 B) 2 C) 4 D) -2 Graph the function. 20) f(x) = e2x 20) A) B) C) D) 6

7 Solve the problem. 21) The function f(x) = ln (x+1) models the average number of free-throws a basketball player 21) can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After 42 days of practice, what is the average number of consecutive free throws the basketball player makes? A) 10 consecutive free throws B) 11 consecutive free throws C) 8 consecutive free throws D) 7 consecutive free throws Graph the function. 22) f(x) = 1 + log x 22) A) B) C) D) 7

8 Solve the problem. 2) ph = -log10[h+] Find the ph if the [H+] = ) A) 7.7 B) 8. C) 7. D) 8.7 Solve the equation. 24) log11 x2 = 4 24) A) {14,641} B) {2 11, -2 11} C) {121, -121} D) {2048} 25) log (x + 2) = -2 25) A) 19 8 B) C) D) 19 9 The graph of a logarithmic function is shown. Select the function which matches the graph. 26) 26) A) y = - log x B) y = log( - x) C) y = log(x - ) D) y = log x - Solve the problem. 27) The number of men dying of AIDS (in thousands) since 1987 is modeled by y = (ln x), 27) where x represents the number of years after Use this model to predict the number of AIDS deaths among men in Express answer rounded to the nearest hundred men. A) 6,900 men B) 25,800 men C) 26,000 men D) 7,000 men Graph the function and its inverse on the same Cartesian plane. 8

9 28) f(x) = log4 x 28) A) B) C) D) Change the logarithmic expression to an equivalent expression involving an exponent. 29) log 6 = x 29) 6 A) 6x = 6 B) 66 = x C) x6 = 6 D) 6x = 6 Solve the equation. 0) e x + 5 = 7 0) A) {ln 7-5} B) {ln 12} C) {e7 + 5} D) {e5} 9

10 Write as the sum and/or difference of logarithms. Express powers as factors. 1) log ) A) log log 17 6 B) log log 17 1 C) log 17 6 log 17 1 D) log log 17 6 Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 2) log25 2) A) 1.10 B) 0.4 C) 2.9 D).22 Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. ) ln e 10 ) A) 10 B) e C) 10 D) 100 Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 4) log 21 4) 5.6 A) 2.64 B) C) 0.17 D).159 Write as the sum and/or difference of logarithms. Express powers as factors. 5) log 19 rs 12 5) A) 1 2 log 19 r log 19 s log B) 1 2 log 19 r log 19 s - log C) 1 2 log 19 r 1 2 log 19 s 1 2 log D) 1 2 log 19 rs log Solve the problem. 6) f(x) = log(x + 6) and g(x) = log(x - 4). 6) Solve g(x) = 129. What point is on the graph of g? A) {5}, (5, 129) B) {125}, (5, 121) C) {5}, (5, 121) D) {125}, (5, 129) Solve the equation. 7) (1 + 2x) = 24 7) A) {2} B) {-2} C) {81} D) {6} Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 8) 5 x + 6 = 7 8) A) {-4.79} B) {-0.6} C) {1.61} D) {6.8} 9) 5x =.8 9) A) {6.08} B) {0.24} C) {0.28} D) {5.57} 10

11 Use a graphing calculator to solve the equation. Round your answer to two decimal places. 40) ln(x) = -x + 40) A) {4.5} B) {.15} C) {1.50} D) {0.15} 11