Algebra Homework!

College Algebra MATH 107 Spring, 2017, V3.2 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, 1]; Range [–2, 4] B. Domain [–2, 4]; Range [–3, 3] C. Domain [–3, 0]; Range [0, 4] D. Domain [–3, 3]; Range [–2, 4] 2. Solve: 11 2 2 x x + = 2. ______ A. 13 B. 1, 7 C. 7 D. No solution 2 4 -4 -2 -4 2 4 -2 College Algebra MATH 107 Spring, 2017, V3.2 Page 2 of 11 3. Determine the interval(s) on which the function is increasing. 3. ______ A. ( ) 1.3, 1.3 B. ( ) , 1 and ( ) 3, C. ( ) 2.5, 1 and ( ) 4.5, D. ( ) 1, 3 4. Determine whether the graph of 2 y x= is symmetric with respect to the origin, the x-axis, or the y-axis. 4. ______ A. symmetric with respect to the origin only B. symmetric with respect to the x-axis only C. symmetric with respect to the y-axis only D. not symmetric with respect to the origin, not s ymmetric with respect to the x-axis, and not symmetric with respect to the y-axis 5. Solve, and express the answer in interval notati on: | 9 – 7x | 12 . 5. ______ A. [–3, 3/7] B. [–3/7, 3] C. (– , 3/7] [3, ) D. (– , –3/7] College Algebra MATH 107 Spring, 2017, V3.2 Page 3 of 11 6. Which of the following represents the graph of 4x 7 y = 28 ? 6. ______ A. B. C. D. College Algebra MATH 107 Spring, 2017, V3.2 Page 4 of 11 7. Write a slope-intercept equation for a line parallel to the line x – 8 y = 3 which passes through the point (16, –5). 7. ______ A. 8 123 y x= + B. 1 3 8 y x= C. 1 5 8 y x= D. 1 7 8 y x= 8. Does the graph below represent a function and is it one-to-one? 8. ______ A. It is a function but not one-to-one. B. It is a function and it is one-to-one.

C. It is not a function and it is not one-to-one. D. It is not a function but it is one-to-one. College Algebra MATH 107 Spring, 2017, V3.2 Page 5 of 11 9. Express as a single logarithm: log a + log 1 – 2 log b. 9. ______ A. ( )b a 2 1 log + B. + b a 2 1 log C.

2 log ab D.

2 log ba 10. Which of the functions corresponds to the graph ? 10. ______ A. ( ) 1 x f x e = + B. ( ) 2 x f x e = + C. ( ) 2x f x e = D. ( ) 2 x f x e = College Algebra MATH 107 Spring, 2017, V3.2 Page 6 of 11 11. Suppose that a function f has exactly one x-intercept. Which of the following statements MUST be true? 11. ______ A. The equation f (x ) = 0 has exactly one real-number solution. B. f is a linear function.

C. f (x ) 0 for all x in the domain of f. D. f is an invertible function.

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 – 2) B. g(x ) = f (x ) – 2 C. g(x ) = f (x – 4) D. g(x ) = f (x + 2) -2 2 4 -4 -2 -4 2 4 -2 2 4 -4 -2 -4 2 4 College Algebra MATH 107 Spring, 2017, V3.2 Page 7 of 11 SHORT ANSWER :

13. Multiply and simplify: (3 + 8 i)(7 + 4 i).

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: 4 0 2 x x + . Answer: ________ 15. Water initially at 190 ° 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 + 120 e – 0.096 t Find the temperature of the water 25 minutes after it is left to cool. (Round to the nearest degree.) Answer: ________ 16. Find the value of the logarithm: 2 1 log 16 . Answer: ________ 17. Solve: 4 57 49 x = . Answer: ________ 18. Suppose $7,600 is invested in an account at an annual interest rate of 4.5% 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 ) = x 2 + 10 x + 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, 2017, V3.2 Page 8 of 11 20. Consider the polynomial P(x ), shown in both standard form and factored form. 4 3 2 1 3 3 13 1 ( ) 3 ( 2)( 1)( 3)( 4) 8 4 8 4 8 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 y-intercept. Answer: ________________ (c) State the zeros of the function. 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, V3.2 Page 9 of 11 21. Let 3 9 ( ) 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 9 ( ) 2 x f x x = ? Answer: ______________ GRAPH A. GRAPH B. GRAPH C. GRAPH D. College Algebra MATH 107 Spring, 2017, V3.2 Page 10 of 11 SHORT ANSWER, with work required to be shown, as indicated .

22. Let 5 ) ( + = x x f and g(x ) = x – 3. (a) Find )1 ( g f . Show work. (b) Find the domain of the quotient function gf . Explain. 23. Points (1, 2) and (–5, 6) are endpoints of the 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 x-axis. 24. Find the equation for a line which passes throu gh the points (4, 7) and (6, –3). Write the equation in slope-intercept form. Show work. 25. A salesperson earns a base salary of $1,560 per month and a commission of 7.8% on the amount of sales. If the salesperson has a paycheck of $4,461.60 for one month, what was the amount of sales for the month? Show work.

26. Let f (x ) = 8 x 2 – 7 and g(x ) = x – 5 .

(a) Find the composite function ) )( ( x g f o and simplify. Show work. (b) Find ( )(3) f go . Show work. 27. Find the exact solutions and simplify as much a s possible: 3x 2 = 6 x + 5 . Show work. 28. Given the function 1 ( ) 8 6 f x x = + , find a formula for the inverse function. Show work. College Algebra MATH 107 Spring, 2017, V3.2 Page 11 of 11 29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by P (x ) = –0.002 x 2 + 4.4x – 1200 (a) What is the company’s profit if 750 donuts are made daily?

(b) How many donuts should be made daily in order t o maximize the company’s profit? Show work. 30. Solve: 2 0 10 32 2 4 x x x = + + + . Show work.