1. Determine the domain and range of the piecewise function. 1. 4...

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1. Determine the domain and range of the piecewise function. 1. 4 2 -4 -2 2 4 2 -4 A. Domain [-4, 2]; Range [-3, 3] B. Domain [-4, 2]; Range [-2, 1] C. Domain [-2, 1]; Range I-4, 2] D. Domain [-3, 3]; Range I-4, 2] 2. Solve: /x+17=3-x - 2. A. -7 B. -1 C. - -1, 8 D. 3. Determine the interval(s) on which the function is increasing. 3. A. (-1,1) and (3,00) 4 B. (-4/3, 1) 2 C. (-00,-5/3), (0,2), and (11/3,00) D. (-00,0) and (2,00) -2 4 -2- 4. Determine whether the graph of = is symmetric with respect to the origin, the x-axis, or the y-axis. 4. A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin B. symmetric with respect to the x-axis only C. symmetric with respect to the y-axis only D. symmetric with respect to the origin only 5. Solve, and express the answer in interval notation: 16-5xl<14. - 5. A. [-8/5, 4] B. (-00, -8/5] U [4, 00) C. (-00,-8/5] D. [4,00) 6. Which of the following represents the graph of 4x - 7y=28? 6. A. B. 10- 10- 5- 5- -10 5. 10 -10 -5. 5 10 -10 -10 C. D. 10- 10- 5 5- -10 5 10 -10 -5 5 10 -5 10 -10 7. Write a slope-intercept equation for a line parallel to the line x+ 5y = 7 which passes through the point (-10, 3). 7. A. y =-5x+53 B. y 5 1 1 C. y= 5 D. >==x+5 1 8. Does the graph below represent a function and is it one-to-one? 8. 4 -2- T A. It is a function and it is one-to-one. B. It is a function but not one-to-one. C. It is not a function but it is one-to-one. D. It is not a function and it is not one-to-one. 9. Express as an equivalent logarithm: log + log 1 - 8log (y+2) 9. x+1 A. log 8(y+2) B. log x log(y+2) x C. log 8 (y+2) D. log (x-8y-15) 10. Which of the functions corresponds to the graph? 10. 8 6 4+ 2- -2 2 4 6 A. f (x) = e-x +2 B. f f(x)=-ex (x) e*+2 = C. +2 D. f(x)=e**+1 = 11. Suppose that a function f has no x-intercepts. Which of the following statements MUST be true? 11. A. f is an invertible function. B. The graph of f has no points whose x-coordinate is 0. C. The graph of f is a horizontal line. D. The equation f (x) = 0 has no real-number solution. 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. 4 4 2 2 -4 -2 2 4 -4 -2 2 4 -2 -2 -4 -4 y = f(x) y=g(x) A. g(x=f(x-2)-1 : B. g(x) =f(x+1)-2 = - C. g(x) =f(x+2)-1 = D. g(x) = f(x + 2) + 2 SHORT ANSWER: 13. Multiply and simplify: (3 + 8i)(5 + 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-6 >0. Answer: x-8 15. A can of soda at 82° F. is placed in a refrigerator that maintains a constant temperature of 35° F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by - t Find the temperature of the soda 10 minutes after it is placed in the refrigerator. (Round to the nearest tenth of a degree.) Answer: 16. Find the value of the logarithm: logs (3) Answer: 17. Solve: 35x-2=9. Answer: 18. Suppose $7,800 is invested in an account at an annual interest rate of 4.3% 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) = x2 - 4x- - (a) Find the vertex. Answer: (b) State the range of the function. Answer: (c) On what interval is the function decreasing? 20. Consider the polynomial P(x), shown in both standard form and factored form. 1 1 7 41 1 P(x) = + + x x+3 = (x+3)(x-D/x-2)(x-5) 10 2 10 10 10 (a) Which sketch illustrates the end behavior of the polynomial function? A. B. C. D. ww 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 10- 10- 5. -4 -4 -2 -5- -5- -10 10- GRAPH C GRAPH D 10 10- 5 5- -4 -2 2 -10 10- 3x-9 21. Let f F(x) = x-2 (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 f(x) = 3x-9 ? Answer: GRAPHA. GRAPH B. 10- 10- 5. 5- -10 -5 5 10 -10 -5 10 -5- -5- -10- -10 GRAPH C. GRAPH D. 10 10- 5- 5- -10 -5 5 10 -10 -5 5 10 -5- -54 -10- -10- SHORT ANSWER, with work required to be shown, as indicated. 22. Let f(x)=Vx-3 = and g(x) = x - 7. - (a) Find work. (b) Find the domain of the quotient function Explain. g 23. Points (-1,8) and (-5, 4) 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 (5,6) and (2,9). Write the equation in slope-intercept form. Show work. 25. A salesperson earns a base salary of $1,960 per month and a commission of 6.8% on the amount of sales. If the salesperson has a paycheck of $4,197.20 for one month, what was the amount of sales for the month? Show work. 26. Let f (x) = 2x2 - 3 and g(x) = X 4. (a) Find the composite function (fog 8)(x) and simplify. Show work. (b) Find (fog)(-1). Show work. 27. Find the exact solutions and simplify as much as possible: 5x2 + 6 = 12x. Show work. 28. Given the function f (x) 1 find formula for the inverse function. Show work. a 29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by P(x)=-0.001 x²+3.2x-1250 = - (a) What is the company's profit if 900 donuts are made daily? (b) How many donuts should be made daily in order to maximize the company's profit? Show work. 30. Solve: x+7 + 24 = 0. Show work. x+3

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