Please review attached document.
Please review attached document.
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. ______ Domain [–3, 3]; Range [0, 3] Domain [–2, 4]; Range [–3, 3] C. Domain [–3, 3]; Range [–2, 4] D. Domain [–1, 4]; Range [–2, 2] 2. Solve: 3x + = −10 x 2. ______ 5 –2, 5 –2 No solution 3. Determine the interval(s) on which the function is decreasing. 3. ______ (–∞, –2) and (4, ∞) (–3.6, 0) and (6.7, ∞) (–1, 3) (–2, 4) the x-axis, or the y-axis. 4. ______ A. symmetric with respect to the x-axis only B. symmetric with respect to the y-axis only 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 Solve, and express the answer in interval notation: | 7 – 8x | ≥ 9. 5. ______ (–∞, −1/4] ∪ [2, ∞) (–∞, –1/4] [–1/4, 2] [–1/4, ∞) Which of the following represents the graph of 9x − 4y = 36 ? 6. ______ B. C. D. Write a slope-intercept equation for a line parallel to the line x – 3y = 8 which passes through the point (– 12, 7). 7. ______ y =− + x 3 y =− −3x 29 y = + x 7 y = + x 11 Does the graph below represent a function and is it one-to-one? 8. ______ It is a function but not one-to-one. It is a function and it is one-to-one. It is not a function and it is not one-to-one. It is not a function but it is one-to-one. Express as a single logarithm: log x – 3 log y + log 1 9. ______ log(x+ −1 3y) x +1 log 3 x +13 log y x D. log 3 y Which of the functions corresponds to the graph? 10. ______ f x( )=− +ex 3 f x( )= e−x +4 f x( )= e−x +3 f x( )= +ex 4 Suppose that for a function f , the equation f (x) = 0 has exactly two real-number solutions. Which of the following statements MUST be true? 11. ______ f has exactly two x-intercepts. f has exactly two y-intercepts. f is an invertible function. f is a quadratic function 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) g(x) = f (x + 1) – 2 g(x) = f (x + 1) – 1 g(x) = f (x + 2) + 2 g(x) = f (x – 1) – 2 SHORT ANSWER: Multiply and simplify: (6 − 5i)(9 + i). Write the answer in the form a + bi, where a and b are real numbers. Answer: ________ x +1 Solve, and write the answer in interval notation: ≤ 0. Answer: ________ x −8 Water initially at 190° F. is left in a room of temperature 70° F to cool. – 0.096 t After t minutes, the temperature T of the water is given by T(t) = 70 + 120e Find the temperature of the water 20 minutes after it is left to cool. (Round to the nearest tenth of a degree.) Answer: ________ 1 16. Find the value of the logarithm: log2 . Answer: ________ 64 Solve: 57 4x− = 25. Answer: ________ Suppose $9,700 is invested in an account at an annual interest rate of 3.2% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________ Let f (x) = x2 + 12x + 39. Find the vertex. Answer: ________ State the range of the function. Answer: ________ On what interval is the function increasing? Answer: ________ Consider the polynomial P(x), shown in both standard form and factored form. P x( ) = x3 −3×2 − + =x 3 (x +1)(x −1)(x −3) Which sketch illustrates the end behavior of the polynomial function? A. B. C. D. vvvv vvvv vvvv vvvv Answer: ________ State the zeros of the function. Answer: ________________ State the y-intercept. Answer: ________________ State which graph below is the graph of P(x). Answer: ________ GRAPH A GRAPH B GRAPH C GRAPH D 3×2 +3 Let f x( ) = 2 . x −4 State the domain. Answer: _________________ State the horizontal asymptote. Answer: _________________ State the vertical asymptote(s). Answer: _________________ 3×2 +3 Which of the following represents the graph of f x( ) = 2 ? Answer: ______________ x −4 SHORT ANSWER, with work required to be shown, as indicated. Let f (x) = 5− x and g(x) = x + 2. Find gf (−4). Show work. f Find the domain of the quotient function . Explain. g 23. Points (2, –5) and (10, –1) are endpoints of the diameter of a circle. What is the length of the diameter? Give the exact answer, simplified as much as possible. Show work. What is the center point C of the circle? Given the point C you found in part (b), state the point symmetric to C about the x-axis. Find the equation for a line which passes through the points (7, 5) and (4, –1) . Write the equation in slope-intercept form. Show work. 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. Let f (x) = 4×2– 7 and g(x) = x + 5. Find the composite function( f οg)( )x and simplify. Show work. Find ( f o g)(−2). Show work. Find the exact solutions and simplify as much as possible: 5×2 + 12 = 20x. Show work. Given the function f x( ) = x −8, find a formula for the inverse function. Show work. 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 + 28.50x – 300 What is the company’s profit if 42 tourists are given the tour? How many tourists should be given the tour in order to maximize the company’s profit? Show work. x +13 84 30. Solve: + = 0. Show work. x +6 x2 −36 Page 13 of 13
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