Solve x 3 2 - x x - 12 0 and write interval notation for

Question

Assignment

1. Solve {(x + 3) (2 - x)} / (x - 1)² > 0 and write interval notation for the solution set.

Show careful algebraic work/explanation.

2. For f(x) = x³ - 4x - 8, use the Intermediate Value Theorem to determine which interval must contain a zero of f(x). (no explanation required) 5. ______

A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4

3. Look at the graph of the quadratic function and state the intercept(s), vertex, and range, and indicate which of equations A, B, C, or D, represents the graph. [No explanations required.]

Graph	Fill in the blanks	Equation
	State the y-intercept(s): ___________ State thevertex: ___________ State therange: _________	The graph represents which of the following equations?   Choice: __ A.    y  =  x2 - 6x + 1 B.    y  =  -x2 - 6x + 1 C.    y  =    x2+6x+1 D.    y  =  -x2+6x + 1

4. Each graph below represents a polynomial function. Complete the following table.

(no explanation required)

Graph	Graph A	Graph B
Is the degree of the polynomial odd or even?(choose one)
Is the leading coefficient of the polynomial positive or negative? (choose one)
How many real number zeros are there?

5. (No explanations required)

Let P(x) = x³ - (21/4)x + (5/2) When factored, P(x) = {x + (5/2)} {x - (1/2)} (x - 2)

(a) State the domain.

(b) Which sketch illustrates the end behavior of the polynomial function?

(c) State the y-intercept:

(d) State the x-intercepts:

(e) State which graph below is the graph of P(x).__________________

6. Let f(x) = (3x² - 3x) / (x² + x - 12) (no explanation required)

(a) State the domain.

(b) State the y-intercept.

(c) State the x-intercept(s).

(d) State the vertical asymptote(s).

(e) State the horizontal asymptote.

7. Solve the equation. Show work in solving

{1 / (5x + 20)} - {1 / (x² - 16)} = {3 / (x - 4)}

8. For z = 5 + 2i and w = 8 - 3i, find z/w. Simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.

9. Find the solutions of the equation 4x² - 8x + 7 = 0. Show algebraic work.

10. The marketing department has found that, when the new model calculators are sold at a price of p dollars per unit, the revenue R (in dollars) as a function of the price is:

R(p) = -150p² + 21,000p

(a) The revenue function is a quadratic function and so its graph is a parabola.

Does the parabola open up or down? _________

(b) What unit price should be established in order to maximize revenue?

(c) If this price is charged, what is the maximum revenue?