College Algebra Test

College Algebra MATH 107 Spring, 2017, V4.12 Page 1 of 11 MATH 107 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually.

Neither collaboration nor consultation with others is allowed. Record your answers and work on the separate answer sheet provided.

There are 30 problems. Problems #1–12 are Multiple Choice.

Problems #13–21 are Short Answer. (Work not require d to be shown) Problems #22–30 are Short Answer with work required to be shown.

MULTIPLE CHOICE 1. Determine the domain and range of the piecewise function. 1. ______ A. Domain [–2, 4]; Range [–3, 3] B. Domain [–3, 3]; Range [–2, 4] C. Domain [–1, 2]; Range [0, 2] D. Domain [–1, 4]; Range [–2, 2] 2. Solve: 2 6 3x x = 2. ______ A. 3 B. 5 C. 3, 5 D. No solution -2 2 4 -4 -2 -4 2 4 College Algebra MATH 107 Spring, 2017, V4.12 Page 2 of 11 3. Determine the interval(s) on which the function is increasing. 3. ______ A. ( )5.0 , and (5, 6.5) B. (– 0.5, 3) C. (–2, 2) D. (1, 5) 4. Determine whether the graph of 7 y x = is symmetric with respect to the origin, the x-axis, or the y-axis. 4. ______ A. symmetric with respect to the x-axis only B. symmetric with respect to the y-axis only C. symmetric with respect to the origin only D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin 5. Solve, and express the answer in interval notati on: 7 3 17 x . 5. ______ A. [–8, 10/3] B. (– , –10/3] C. [–10/3, 8] D. (– , –10/3] [8, ) College Algebra MATH 107 Spring, 2017, V4.12 Page 3 of 11 6. Which of the following represents the graph of 3x + 7 y = 21 ? 6. ______ A. B.

C. D. College Algebra MATH 107 Spring, 2017, V4.12 Page 4 of 11 7. Write a slope-intercept equation for a line parallel to the line x – 5 y = 9 which passes through the point (–10, 3). 7. ______ A. 1 5 5 y x= + B. 1 3 5 y x= + C. 1 3 5 y x= + D. 5 53 y x= + 8. Does the graph below represent a function and is it one-to-one? 8. ______ A. It is a function and it is one-to-one. B. It is a function but not one-to-one.

C. It is not a function but it is one-to-one.

D. It is not a function and it is not one-to-one. College Algebra MATH 107 Spring, 2017, V4.12 Page 5 of 11 9. Express as an equivalent expression: 8 log (x – 3) + log 1 – log y 9. ______ A. 8 log( 3) log( ) x y B. ( ) 8 3 log x y C. 8 24 log x y D. ( ) log 8 23 x y 10. Which of the functions corresponds to the graph ? 10. ______ A. ( ) 1 x f x e = B. ( ) x f x e = C. ( ) 1 x f x e = + D. ( ) 1 x f x e + = College Algebra MATH 107 Spring, 2017, V4.12 Page 6 of 11 11. Suppose that for a function f , the equation f (x ) = 0 has exactly three real-number solutions.

Which of the following statements MUST be true? 11. ______ A. f is an invertible function.

B. f is a polynomial of degree 3.

C. f has exactly three x-intercepts. D. f has exactly three y-intercepts.

12. The graph of y = f (x ) is shown at the left and the graph of y = g(x ) is shown at the right. (No formulas are given.) What is the relationship betwe en g(x ) and f (x )? 12. ______ y = f (x ) y = g(x ) A. g(x ) = f (x + 1) – 2 B. g(x ) = f (x – 1) + 2 C. g(x ) = f (x – 2) + 1 D. g(x ) = f (x + 2) + 1 2 4 -2 -4 -2 -4 2 4 2 4 -2 -4 -2 -4 2 4 College Algebra MATH 107 Spring, 2017, V4.12 Page 7 of 11 SHORT ANSWER : 13. Multiply and simplify: (6 + 5i) 2.

Write the answer in the form a + bi, where a and b are real numbers. Answer: ________ 14. Solve, and write the answer in interval notatio n: 1 0 6 x x + . Answer: ________ 15. Water initially at 130 ° F. is left in a room of temperature 70 ° F to cool.

After t minutes, the temperature T of the water is given by T (t) = 70 + 60 e – 0.096 t Find the temperature of the water 14 minutes after it is left to cool. (Round to the nearest degree.) Answer: ________ 16. Find the value of the logarithm: 4 1 log 16 . Answer: ________ 17. Solve: 6 19 81 x = . Answer: ________ 18. Suppose $4,000 is invested in an account at an annual interest rate of 3.3% compounded continuously. How long (to the nearest tenth of a y ear) will it take the investment to double in size? Answer: ________ 19. Let f (x) = x2 + 4 x 3 . (a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ____ ____ (c) On what interval is the function decreasing? Answer: ________ College Algebra MATH 107 Spring, 2017, V4.12 Page 8 of 11 20. Consider the polynomial P(x ), shown in both standard form and factored form. 4 3 2 1 1 7 1 1 ( ) 3 ( 3)( 1)( 1)( 2) 2 2 2 2 2 P x x x x x x x x x = + + = + + (a) Which sketch illustrates the end behavior of th e polynomial function? Answer: ________ (b) State the zeros of the function. Answer: ________________ (c) State the y-intercept. Answer: ________________ (d) State which graph below is the graph of P(x ). Answer: ________ GRAPH A GRAPH B GRAPH C GRAPH D A. B. C. D. vvv v vvv v vvv v vvv v College Algebra MATH 107 Spring, 2017, V4.12 Page 9 of 11 21. Let 3 1 ( ) 2 x f x x + = . (a) State the domain. Answer: _________________ (b) State the horizontal asymptote. Answer: _________________ (c) State the vertical asymptote(s). Answer: _________________ (d) Which of the following represents the graph of 3 1 ( ) 2 x f x x + = ? Answer: ______________ GRAPH A. GRAPH B. GRAPH C. GRAPH D. College Algebra MATH 107 Spring, 2017, V4.12 Page 10 of 11 SHORT ANSWER, with work required to be shown, as indicated .

22. Let f (x) = x – 1 and 9 ) ( + = x x g . (a) Find )5 ( gf. Show work. (b) Find the domain of the quotient function g f . Explain. 23. Points (–8, 3) and (–2, 7) are endpoints of th e diameter of a circle.

(a) What is the length of the diameter? Give the ex act answer, simplified as much as possible.

Show work.

(b) What is the center point C of the circle? (c) Given the point C you found in part (b), state the point symmetric t o C about the y-axis. 24. Find the equation for a line which passes throu gh the points (4, 1) and (6, –5). Write the equation in slope-intercept form. Show work. 25. A salesperson earns a base salary of $1,540 per month and a commission of 7.6% on the amount of sales made. If the salesperson has a payc heck of $4,086 for one month, what was the amount of sales for the month? Show work.

26. Let f (x ) = 4 x 2 + 5 and g(x ) = x – 3.

(a) Find the composite function ) )( ( x g f o and simplify. Show work. (b) Find ( )(1) f go . Show work. 27. Find the exact solutions and simplify as much a s possible: 3x2 = 8 + 8 x. Show work. 28. Given the function 1 ( ) 2 3 f x x = , find a formula for the inverse function. Show work. College Algebra MATH 107 Spring, 2017, V4.12 Page 11 of 11 29. Chocolate Confections, Inc. has determined that when x chocolate cakes are made daily, the average cost per chocolate cake, in dollars, is giv en by C( x) = 0.001 x2 – 0.14 x + 12.70 (a) What is the average cost per cake if 30 chocola te cakes are made daily?

(b) How many chocolate cakes should be made daily i n order to minimize the average cost per cake? Show work.

30. Solve: 2 0 11 60 6 36 x x x = + . Show work.