College Algebra MATH 107 Summer, 2017, V1.6 SHORT ANSWER: 13. Multiply and simplify: (4 + 7i)2. Write the answer in the form a + bi, where a and b are real numbers. 14. Solve, and write the answer in interval notation: x+5 0. x +1 Answer: ________ Answer: ________ 15. A can of soda at 81 F. is placed in a refrigerator that maintains a constant temperature of 38 F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by T(t) = 38 + 43e - 0.058 t Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the nearest tenth of a degree.) Answer: ________ 1 16. Find the value of the logarithm: log8 . 64 17. Solve: 76 x+1 = 49 . Answer: ________ Answer: ________ 18. Suppose $9,400 is invested in an account at an annual interest rate of 3.5% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________ 2 19. Let f (x) = x + 8x + 9. (a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function increasing? Answer: ________ Page 7 of 11 College Algebra MATH 107 Summer, 2017, V1.6 20. Consider the polynomial P(x), shown in both standard form and factored form. 1 7 7 1 P ( x) = x3 + x 2 x 5 = ( x + 1)( x 3)( x 5) 3 3 3 3 (a) Which sketch illustrates the end behavior of the polynomial function? B. A. vvvv C. vvvv D. vvvv vvvv Answer: ________ (b) State the zeros of the function. Answer: ________________ (c) State the y-intercept. Answer: ________________ Answer: ________ (d) State which graph below is the graph of P(x). GRAPH A GRAPH B GRAPH C GRAPH D Page 8 of 11 College Algebra MATH 107 21. Let f ( x) = Summer, 2017, V1.6 3x 2 3 . x2 4 (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 f ( x) = 3x 2 3 ? x2 4 GRAPH A. GRAPH B. GRAPH C. GRAPH D. Answer: ______________ Page 9 of 11 College Algebra MATH 107 Summer, 2017, V1.6 SHORT ANSWER, with work required to be shown, as indicated. 22. Let f ( x) = x 4 and g(x) = x 8. f (a) Find (13) . Show work. g (b) Find the domain of the quotient function f . Explain. g 23. Points (-5, 2) and (1, 8) 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 point C of the circle? (c) 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 (- 6, 3) and (- 4, -9). Write the equation in slope-intercept form. Show work. 25. Pete, a resident of Metropolis, pays Metropolis an annual tax of $70 plus 1.8% of his annual income. If Pete paid $1,186 in tax, what was Pete's income? Show work. 26. Let f (x) = 2x2 - 7 and g(x) = x - 6. (a) Find the composite function ( f o g )( x) and simplify. Show work. (b) Find ( f o g ) (5) . Show work. 2 27. Find the exact solutions and simplify as much as possible: 2x = 8x + 3. Show work. 28. Given the function f ( x) = 7 + 1 x , find a formula for the inverse function. Show work. 6 Page 10 of 11 College Algebra MATH 107 Summer, 2017, V1.6 29. The Travel Time bus company has determined that when x tourists are given a particular bus tour, the profit P, in dollars, is given by P(x) = -0.25 x2 + 24.50x - 160 (a) What is the company's profit if 32 tourists are given the tour? (b) How many tourists should be given the tour in order to maximize the company's profit? Show work. 30. Solve: x + 11 48 + 2 = 0 . Show work. x +3 x 9 Page 11 of 11