College Algebra Math 107 Spring 2015 V48page 1 Of 11math 107 Fi ✓ Solved

College Algebra MATH 107 Spring, 2015, V4.8 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 required 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 [0, 4]; Range [–1, 3] B. Domain [–1, 3]; Range [0, 4] C. Domain [–1, 0]; Range [1, 4] D. Domain [–1, 1]; Range [1, 4] 2.

Solve: 19 3 3x x− = − 2. ______ A. No solution B. 8 C. −2, 5 D. − College Algebra MATH 107 Spring, 2015, V4.8 A. ( ), 0.5−∞ − and (3, 6.5) B. [– 2, 2] C. (1, 5) D. ( ), 1−∞ and ( )5, ∞ 4. Determine whether the graph of 2xy += 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 notation: | 7 – 3x | ≤ 11. 5. ______ A. [–4/3, 6] B. (–∞, –4/3] C. (–∞, –4/3] ∪ [6, ∞) D. (–∞, 6] ∪ [–4/3, ∞) College Algebra MATH 107 Spring, 2015, V4.8 A. B. C. D.

College Algebra MATH 107 Spring, 2015, V4.8 the point (– 12, 7). 7. ______ A. y x= + B. y x= − + C. 3 29y x= − − D. y x= + 8. Which of the following best describes the graph? 8. ______ A.

It is the graph of a function and it is one-to-one. B. It is the graph of a function but not one-to-one. C. It is not the graph of a function.

D. It is the graph of a parabolic relation. College Algebra MATH 107 Spring, 2015, V4.8 A. 3 log( 2) log x y + B. ( )log 3 3x y+ − C. 3 2 log x y  +   ï£ ï£¸ D.

3 log 3 x y  +   ï£ ï£¸ 10. Which of the functions corresponds to the graph? 10. ______ A. ( ) 3xf x e−= + B. ( ) 3xf x e= + C. ( ) 3xf x e= − + D. ( ) 2xf x e−= + College Algebra MATH 107 Spring, 2015, V4.8 answered 27 questions correctly and earned a score of 36%. What would Bob’s percentage score have been if he had answered 48 questions correctly? 11. ______ A.

75% B. 57% C. 64% D. 45% 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 between g(x) and f (x)?

12. ______ y = f (x) y = g(x) A. g(x) = f (x – 2) – 1 B. g(x) = f (x – 2) + 1 C. g(x) = f (x + 2) + 1 D. g(x) = f (x – 1) + College Algebra MATH 107 Spring, 2015, V4.8 SHORT ANSWER: 13. Multiply and simplify: (9 – 4i)(1 + 2i). Write the answer in the form a + bi, where a and b are real numbers. Answer: ________ 14. Solve, and write the answer in interval notation: x x + ≤ − .

Answer: ________ 15. A bowl of soup at 195° F. is placed in a room of constant temperature of 65° F. The temperature T of the soup t minutes after it is placed in the room is given by T(t) = 65 + 130 e – 0.075 t Find the temperature of the soup 6 minutes after it is placed in the room. (Round to the nearest degree.) Answer: ________ 16. Find the value of the logarithm: 2 1 log 16     ï£ ï£¸ . Answer: ________ 17.

Solve: x + = . Answer: ________ 18. Suppose ,500 is invested in an account at an annual interest rate of 7.3% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________ 19.

Let f (x) = x 2 −−−− 10x + 33. (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, 2015, V4.8 P x x x x x x x x x= − − + + − = − + + − − (a) Which sketch illustrates the end behavior of the 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. vvvv vvvv vvvv vvvv College Algebra MATH 107 Spring, 2015, V4.8 x f x x − = − . (a) State the domain. Answer: _________________ (b) State the vertical asymptote(s). Answer: _________________ (c) State the horizontal asymptote. Answer: _________________ (d) Which of the following represents the graph of x f x x − = − ? Answer: ______________ GRAPH A.

GRAPH B. GRAPH C. GRAPH D. College Algebra MATH 107 Spring, 2015, V4.8 SHORT ANSWER, with work required to be shown, as indicated. 22.

Simplify: ( ) a b a b b − − − . Show work. 23. Points (6, 5) and (4, –9) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplified as much as possible.

Show work. (b) What is the center of the circle? (c) What is the equation of the circle? 24. Find the equation for a line which passes through the points (–5, 9) and (–1, 1) . Write the equation in slope-intercept form. Show work.

25. A salesperson earns a base salary of ,820 per month and a commission of 6.5% on the amount of sales. If the salesperson has a paycheck of