8/14 OL1 1. Solve the inequality |42 x|8 and write the solution set in interval notation. Select one of the multiple choice answers. Show work. A. B. C. D. 2. Solve [-2, ) (-, -2] [6, ) (-, 6] [-2, ) [-2, 6] x +3 x1 0 and write the solution set in interval notation. Select one of the multiple choice answers. Show work. A. B. C. D. [-3, 1) (-, -3] (-, -3] (1, ) (1, ) 3. For f (x) = x3 + x2 - 4, use the Intermediate Value Theorem to determine which interval must contain a zero of f. Select one of the answers. Show work. A. B. C. D. Between 0 and 1 Between 1 and 2 Between 2 and 3 Between 3 and 4 8/14 OL1 4. Consider the graph of the quadratic function. Find the following: (a) State the vertex (b) State the range (c) State the interval on which the function is decreasing (d) Select which of these equations represents the graph. A. y = -x2 + 2x -1 B. y = -2x2 - 4x + 1 C. y = 2x2 + 4x -1 D. y = x2 + 2x - 1 5. Let 4x 2 4 f ( x) 2 x 9 . (no explanations required) (a) State the y-intercept. (b) State the x-intercept(s). (c) State the vertical asymptote(s). (d) State the horizontal asymptote. 6. Solve the equation. Check all proposed solutions. Show work. x 1 6 2 0 x 2 x 2x 7. Simplify the term 1+3 i 2i Write the result in the form a + bi, where a and b are real numbers. Show work. 8. Consider the equation 3x2 + 2 = 4x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show work. 9. The cost (C) for a company to produce x widgets is given by C(x) = 5250 + 7.0 x. The company has determined that the profit (P) for x widgets is given by P(x) = 0.02 x2 + 38.0 x 5250. (a) What is the Cost (C) to produce 500 widgets and what is the Profit (P)? Show work. 8/14 OL1 (b) Find the vertex of the profit function P(x) using algebra. Your answer should be a point (x,P). Describe what this point represents? Show work. 8/14 OL1 10. Let P ( x )=x 3 +4.5 x 20.5 x6 When factored, ( 32 ) ( x4 ) P ( x )=( x +1 ) x (a) State the domain. (b) Which sketch illustrates the end behavior of the polynomial function? Select one answer. A. B. vvvv C. vvvv D. vvvv vvvv (c) State the y-intercept. (d) State the real zeros. (e) State which graph below is the graph of P(x). Select one answer. GRAPH A. (below) GRAPH B. (below) GRAPH C. (below) GRAPH D. (below) 8/14 OL1 \f\fInterval Notation I have another question to a problem that I just posted What steps are missing in the problem of the attached file? I was told that I need to test combinations of the terms that will yield a negative result. Here are the intervals I need to test. Pick one number in each interval and see if it works in the equation. Once this is done, you have the solution. x<-3 -33 there are 5 intervals to test, and only two of them will work. \f\fInterval Notation I have another question to a problem that I just posted What steps are missing in the problem of the attached file? I was told that I need to test combinations of the terms that will yield a negative result. Here are the intervals I need to test. Pick one number in each interval and see if it works in the equation. Once this is done, you have the solution. x<-3 -33 there are 5 intervals to test, and only two of them will work