Please solve
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I have completed this assignment myself; working independently and not consulting anyone except the instructor.
Write your name here:
Multiple-choice: Select the correct answer and write it in the space provided. Do not show work; write only one of the letters A, B, C, or D.
A. 2 B. 3 C. 4 D. 5
6. Ans: _C___
7. Ans: __B___
A. x=2 B. x=-2 C. x=-4 D. x=4
A. x=2 B. x=-2 C. x=-1 (Should be y=-1) D. x=1
13. (4 pts) Let f (x) = -2x3+4x2-x+1. Use the Intermediate Value Theorem to determine which interval must contain a zero of f(x).
13. Ans: __B___
A. Between 0 and 1 B. Between 1 and 2 C. Between 2 and 3 D. Between 3 and 4
14. (4 pts) True or False: Let y=f(x) be a polynomial function. The x-intercepts of the function f(x) are the roots of the equation f(x) = 0.
14: Ans._____
15. (4 pts) True or False. Let y=f(x) be a polynomial function of degree 3.
The function y=f(x) must have at least one real root. 15. Ans: ____
16. (4 pts) True or False. It is possible for a quadratic equation with real coefficients to have one real and one complex root.
16. Ans: ____
17. (6 pts) Consider the graph of the polynomial y=p(x). Answer the following questions. (No explanation needed)
(a) Is the degree of p(x) even or odd? Ans: _____
(b) Is the leading coefficient positive or negative? Ans. ______
(c) How many real number zeros are there? Ans: _____
(a) State the y-intercept.
(b) State the x-intercept(s).
(c) State the vertical asymptote(s).
(d) State the horizontal asymptote.
(e) Draw the graph. Show the asymptotes.
19. (5 pts). Translate this sentence about area into a mathematical equation.
The area A of a regular hexagon is directly proportional to the square of the length s of its side.
20. (10 pts). Find all solutions, real and complex, of the equation x2-4x+5=0.
Simplify as much as possible and clearly show all the steps.
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