PRECALCULUS I/MATH 126 (2188) SHANNON MYERS
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1 PRECALCULUS I/MATH 126 (2188) SHANNON MYERS π 100 POINTS POSSIBLE π YOUR WORK MUST SUPPORT YOUR ANSWER FOR FULL CREDIT TO BE AWARDED π YOU MAY USE A SCIENTIFIC AND/OR A TI-83/84/85/86 CALCULATOR π PROVIDE EXACT ANSWERS UNLESS OTHERWISE INDICATED π PLEASE MAKE SURE YOU ARE TAKING THE CORRECT EXAM! ONCE YOU BEGIN THE EXAM, YOU MAY NOT LEAVE THE PROCTORING CENTER UNTIL YOU ARE FINISHED THIS MEANS NO BATHROOM BREAKS! NAME 1
2 MATH 126/PRECALCULUS I/MYERS NAME EXAM 2/100 POINTS POSSIBLE YOUR GRAPHING CALCULATOR SHOULD ONLY BE USED TO CHECK YOUR RESULTS. CREDIT WILL BE AWARDED BASED ON WORK SHOWN. THERE WILL BE NO CREDIT FOR GUESSING. PLEASE PRESENT YOUR WORK IN AN ORGANIZED, EASY TO READ FASHION. 1. (6 POINTS) The point at which a company s profits equal zero is called the company's break even point. Let R represent a company's revenue, let C represent the company's costs, and let x represent the number of units produced and sold each day. 16x and C x 2.25x 12,000 R x a. Find the firm's break even point. b. Find the number of units the company must sell to earn a profit f ( x) 5x 2x 1. a. (2 POINTS) Determine, without graphing, whether the given polynomial function has a maximum value or minimum value. Explain. b. (4 POINTS) Find the minimum value or maximum value without using your graphing calculator. Do not use your graphing calculator and show all work. 2
3 3. (8 POINTS) Solve the following inequality. Do not use your graphing calculator and show all work. 2x 7 1 x 10 3
4 f( x) x (15 POINTS) Consider the quadratic function (4 POINTS) Solve 2 a. (4 POINTS) Find the zeros of f. b. (2 POINTS) Find the y intercept. c. (4 POINTS) Find the vertex. d. (2 POINTS) What is the axis of symmetry? e. (3 POINTS) Sketch the graph of f by hand using the information from parts a d. Be sure to label your graph. 4
5 5. (13 POINTS) Consider The function f x a. (3 POINTS) If possible, simplify f. 2 x 2x 8. 2 x 4 b. (4 POINTS) What is the domain of f? Please describe how any domain restrictions appear on the graph of f. c. (2 POINTS) Find the vertical asymptote(s) of f. If there are no vertical asymptotes, write none. d. (2 POINTS) Find the horizontal asymptote(s) of f. If there are no horizontal asymptotes, write none. e. (2 POINTS) Find the oblique (slant) asymptote of f. If there is no oblique asymptote, write none. 5
6 6. (10 POINTS) Form a polynomial f x with real coefficients having the given degree and zero. Degree 4; zeros: 5, 2i 6
7 f x 2x 5x x 5x (12 POINTS) Consider the function a. (2 POINTS) Use the rational zeros theorem to list the potential rational zeros of the polynomial function. b. (10 POINTS) Find the real zeros of f without using your graphing calculator.. 7
8 (30 POINTS)Consider the polynomial function f x 2x 3 x 1 a. ( 2 POINTS) Determine the end behavior of the graph of the function: The graph of f behaves like y = for large values of x. b. (4 POINTS) Find the x intercept(s), if any. Do not use your graphing calculator and show all work. c. (2 POINTS) Find the y intercept, if any. d. (9 POINTS) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x axis. i. The zero(s) of f are. ii. f has a zero of multiplicity, at x the x axis at x =. iii. f has a zero of multiplicity, at x the x axis at x =. so the graph of f so the graph of f e. (3 POINTS) Use your graphing calculator to approximate the turning point(s) of the graph. Round the coordinates to 2 decimal places. f. (2 POINTS) Find the domain of the function. You may use either interval or set builder notation. g. (2 POINTS) Find the range of the function. You may use either interval or set builder notation. h. (6 POINTS) Use the graph to determine where the function is increasing or decreasing. Give your results in interval notation. i. On which interval(s) is the function increasing? Round the coordinates to 2 decimal places. 8 ii. On which interval(s) is the function decreasing? Round the coordinates to 2 decimal places.
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x 2 + 3, r 4(x) = x2 1
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