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College Algebra MATH 107 Fall, 2019, V1.17 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 #1712 are Multiple Choice. Problems #13721 are Short Answer. (Work not required to be shown) Problems #2230 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 [71, 0]; Range [1, 4] C. Domain [71, 1]; Range [1, 4] D. Domain [71, 3]; Range [0, 4] 2. Solve: x+l7=3x 2. A. No solution B. 7 C. l D. l, 8 Page 1 ofll College Algebra MATH 107 Fall, 20 19, V1.17 3. Determine the interval (s) on which the function is decreasing. 3. 4+ -2 -2+ -4+ A. (-0.5, 3 ) B. (-co, 1) and (5, co ) C. (1, 5) D. (3, 6.5) 4. Determine whether the graph of Y = 3x-5 is symmetric with respect to the origin, the x-axis, or the y-axis. 4. symmetric with respect to the x-axis only symmetric with respect to the y-axis only D symmetric with respect to the origin only 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: |9 -6x | 23. 5. A. [1, 2] B. [1, 00) C. (-co, 2] ) log *+1 y 10. Which of the functions corresponds to the graph? 10. 10 24 -2 + A. f(x)=e*+4 B. f ( x)=2*+4 C. f(x)=e-*+3 D. f(x)=-e*+3 Page 5 of 11College Algebra MATH 107 Fall, 2019, V1.17 11. Suppose that for a function f, the equation f (x) = 0 has exactly one real-number solution. Which of the following statements MUST be true? 11. A. f has exactly one xintercept. B. f is an invertible function. C. f is a linear function. D. There is exactly one point on the graph off which has an xcoordinate of 0. 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(x1)+2 B. g(x):f(x2)l 0- 5-206) :fOCeZ) " 1 D. g(x) =f(x + 2) "1 Page 6 ofll College Algebra MATH 107 Fall, 2019, V1.17 SHORT ANSWER: 13. Multiply and simplify: (5 + 41')(3 21'). 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+20. Answer: xS 15. Water initially at 180 F. is left in a room of temperature 70 F to 0001. After I minutes, the temperature T of the water is given by T(t)=70+110e'0-096i Find the temperature of the water 10 minutes after it is left to cool. (Round to the nearest degree.) Answer: 16. Find the value of the logarithm: log8 (5]. Answer: 17. Solve: 46x7 5 =16. Answer: 18. Suppose $5,000 is invested in an account at an annual interest rate of 3.7% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: 19. Letf(x) = x2 + 14x + 52. (a) Find the vertex. Answer: (b) State the range of the function. Answer: (0) On What interval is the function decreasing? Answer: Page 7 ofll College Algebra MATH 107 Fall, 2019, V1.17 20. Consider the polynomial P(x), shown in both standard form and factored form. P ( x ) x - 2x - 3x7+2x+6=-(x+3)(x+1)(x-2)(x-5) (a) Which sketch illustrates the end behavior of the polynomial function? A A B. D. Answer : (b) State the y-intercept. Answer : (@) State the zeros of the function. Answer: (d) State which graph below is the graph of P(x). Answer: GRAPH GRAPH A 10- B 10- - 10 GRAPH C 10 GRAPH D -10. -15- Page 8 of 11College Algebra MATH 107 Fall, 2019, V1.17 21. Let f(x) = 3x-9 x- 2 (@) 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 / (x) =- 3x- 2 ? x- 2 Answer: GRAPH A GRAPH B. 10- -10 10 -10 10 10- GRAPH C. GRAPH D. + -10 5 -10 10 Page 9 of 11College Algebra MATH 107 Fall, 2019, V1.17 SHORT ANSWER, with work required to be shown, as indicated. 22. Let f(x) =x+ l and g(x)=\\/7x. (a) Find [f](9). Show work. 8 (b) Find the domain of the quotient function i. Explain. g 23. Points (1, 6) and (,7, 8) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplied as much as possible. Show work. (b) What is the center point C of the circle? (0) Given the point C you found in part (b), state the point symmetric to C about the y-axis. 24. Find the equation for a line which passes through the points (, 1, 2) and (, 4, 11). Write the equation in slope-intercept form. Show work. 25. A salesperson earns a base salary of $1,520 per month and a commission of 5.5% on the amount of sales. If the salesperson has a paycheck of $4,957.50 for one month, what was the amount of sales for the month? Show work. 26. Letf(x) = 3x2 + 8 and g(x) = x 4. (a) Find the composite functioan Og)(x) and simplify. Show work. (b) Find (f og)(l). Show work. 27. Find the exact solutions and simplify as much as possible: 12x2 + 5 : 20x. Show work. 28. Given the function f(x) = 3 lx , find a formula for the inverse function. Show work. 8 Page 10 of11 College Algebra MATH 107 Fall, 2019, V1.17 29. The Travel Time bus company has determined that When x tourists are given a particular bus tour, the prot P is given by P(x) = 0.25 x2 + 28.50x 310 (a) What is the company's prot if 38 tourists are given the tour? (b) How many tourists should be given the tour in order to maximize the company's prot? Show work. x+9 36 + 30. Solve: x+6 x2 36 = 0 . Show work. Pagellofll