Please answer the following questions correctly on the question sheets. Both are attached.
College Algebra MATH 107 Spring, 20 20, V : s20 Page 1 of 13 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 consultati on 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 [ –4, 0]; Range [ –2, 2] B. Domain [ –4, 0]; Range [0, 2] C. Domain [ –2, 2]; Range [ –4, 0] D. Domain [0, 2]; Range [ –4, 0] 2. Solve: 10 − = − 3x x 2. ______ A. –5, 2 B. –5 C. 5/2 2 4 -4 - 2 -4 2 4 - 2 College Algebra MATH 107 Spring, 20 20, V : s20 Page 2 of 13 D. No solution 3. Determine the interval(s) on which the function is increasing. 3. ______ A. (–∞ , – 4) and (2, ∞ ) B. (–6.7, 0) and (3.6, ∞ ) C. (– 4, 2) D. (–1, 3) the x-axis, or the y-axis. 4. ______ A. not symmetric with respect to the y- axis, not symmetric with respect to the x-axis, and not symmetric with respect to the origin 4 . Determine whether the graph of 1 3 y x −= = is symmetric with respect to the origin, College Algebra MATH 107 Spring, 20 20, V : s20 Page 3 of 13 B. symmetric with respect to the origin only C. symmetric with respect to the x-axis only D. symmetric with respect to the y-axis only 5. Solve, and express the answer in interval notation: | 7 – 3x | ≤ 11 . 5. ______ A. (–∞ , –4/3] B. [–4/3, 6] C. (–∞ , –4/3] ∪ [6, ∞ ) D. (–∞ , 6] ∪ [–4/3, ∞ ) 6. Which of the following represents the graph of 9 x − 4y = 36 ? 6. ______ A. B. C. D. College Algebra MATH 107 Spring, 20 20, V : s20 Page 4 of 13 7. Write a slope -intercept equation for a line parallel to the line x – 6y = 12 which passes through the point ( –18, 7). 7. ______ A. y = x +10 B. y = x +7 C. y =− − 6x 101 D. y =− + x 4 8. Does the graph below represent a funct ion and is it one -to-one? 8. ______ College Algebra MATH 107 Spring, 20 20, V : s20 Page 5 of 13 A. It is not a function but it is one -to-one. B. It is a function and it is one -to-one. C. It is a function but not one -to-one. D. It is not a function and it is not one -to-one. 9. Express as an equivalent expression: log x + log 1 – 8 log ( y + 2) 9. ______ x A. log 8 ( y + 2) log x B. 8 log( y + 2) x +1 C. log 8(y + 2) D. log (x− −8y 15 ) 10. Which of the functions corresponds to the graph? 10. ______ College Algebra MATH 107 Spring, 20 20, V : s20 Page 6 of 13 A. f x ( ) =− − ex 1 B. f x ( ) = e−x −1 C. f x ( ) = − ex 1 D. f x ( ) = e−x −2 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 has exactly three x-intercepts. B. f has exactly three y-intercepts. C. f is a polynomial of degree 3. D. f is an invertible function. College Algebra MATH 107 Spring, 20 20, V : s20 Page 7 of 13 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 + 1 ) + 4 B. g(x) = f (x + 4) + 3 C. g(x) = f (x – 4) + 1 D. g(x) = f (x + 1) + 2 SHORT ANSWER : 13. Multiply and simplify: (3 + 4 i)(6 − 7i). Write the answer in the form a + bi, where a and b are real nu mbers. Answer: ________ x +9 14. Solve, and write the answer in interval notation: ≤ 0. Answer: ________ x −4 2 4 -2 -4 - 2 -4 2 4 2 4 -2 -4 - 2 -4 2 4 College Algebra MATH 107 Spring, 20 20, V : s20 Page 8 of 13 15. Water initially at 190 ° F. is left in a room of temperature 60 ° F to cool. – 0.096 t After t minutes, the temperature T of the water is given by T(t) = 60 + 130 e Find the temperature of the water 30 minutes after it is left to cool. (Round to the nearest degree.) Answer: ________ 1 16. Find the value of the logarithm: log 3 . 9 Answer: ________ 17. Solve: 53 8 x− = 25 . Answer: ________ 18. Suppose $7,200 is invested in an account at an annual interest rate of 4.5% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________ 2 20. Consider the polynomial P(x), shown in both standard form and factored form. 1 3 3 2 13 1 P x ( ) =− x − x + x + =− 3 (x −3)( x +1)( x +5) 5 5 5 5 (a) Which sketch illustrates the end behavior of the polynomial function? 19. Let f (x) = x + 10 x + 32. (a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function decreasing? Answer: ________ A. B. C. D. College Algebra MATH 107 Spring, 20 20, V : s20 Page 9 of 13 Answer: ________ (b) State the y-intercept. Answer: ________________ (c) State the zeros of the functio n. Answer: ________________ (d) State which graph below is the graph of P(x). Answer: ________ GRAPH A GRAPH B GRAPH C GRAPH D vvvv vvvv vvvv vvvv College Algebra MATH 107 Spring, 20 20, V : s20 Page 10 of 13 3x2 +3 21. Let f x ( ) = 2 . x −4 (a) State the domain. Answer: _________________ (b) State the horizontal asymptote. Answer: _________________ (c) State the vertical asymptote(s). Answer: _________________ 3x2 +3 (d) Which of the following represents the graph of f x ( ) = 2 ? Answer: ______________ x −4 GRAPH A. GRAPH B. College Algebra MATH 107 Spring, 20 20, V : s20 Page 11 of 13 GRAPH C. GRAPH D. SHORT ANSWER, with work required to be shown, as indicated . 22. Let f (x) = x + 2 and g(x) = 5 − x . (a) Find gf (−4). Show work. f College Algebra MATH 107 Spring, 20 20, V : s20 Page 12 of 13 (b) Find the domain of the quotient function . Explain. g 23. Points (2, 1) and (6, –3) are endpoin ts 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 point C of the circle? (c) Given the point C you found in part (b), state the point symmetric to C abo ut the x-axis. 24. Find the equation for a line which passes through the points (3, –5) and ( –1, 1). Write the equation in slope -intercept form. Show work. 25. A salesperson earns a base sa lary of $2,100 per month and a commission of 6.5% on the amount of sales made. If the salesperson has a paycheck of $3,699 for one month, what was the amount of sales for the month? Show work. 26. Let f (x) = 3 x2 + 7 and g(x) = x – 3. (a) Find the composite function( f οg)( ) x and simplify. Show work. (b) Find ( f og)( 2) − . Show work. 27. Find the exact solutions and simplify as much as possible: 7x2 + 2 = 8 x. Show work. College Algebra MATH 107 Spring, 20 20, V : s20 Page 13 of 13 28. Given the function f x ( ) = − 4 x , find a formula for the inverse function. Show work. 29. Dream Donuts, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by P(x) = –0.002 x2 + 4.1 x – 1200 (a) What is the company’s profit if 600 donuts are made daily? (b) How many donuts should be made daily in order to maximize the company’s profit? Show work. x+9 40 30. Solve: + 2 = 0. Show work. x+4 x −16
