Assignment

Part 1

1. Solve the inequality x² ≥ 7xand write the solution set in interval notation.
(no explanation required)
A. [7, ∞)
B. (-∞, 0] ∪ [7, ∞)
C. (-∞, 7] ∪ [0, ∞)
D. [0, 7]

2. Solve (x + 3)/(x^(2)- 7x + 6) ≤ 0 and write the solution set in interval notation.
(no explanation required)
A. (1, 6)
B. (-∞,-3]
C. (-∞,-3] ∪(1, 6)
D. [-3, 1) ∪ (6, ∞)

3. Forf(x) = x³ - 2x² - 7, use the Intermediate Value Theorem to determine which interval must contain a zero of f.(no explanation required)
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4

4. Translate this sentence about area into a mathematical equation.

The area A of a regular pentagon is directly proportional to the square of the length s of its sides.

5. Look at the graph of the quadratic function and complete the table.[No explanations required.] Graph Fill in the blanks Equation

6. Each graph below represents a polynomial function. Complete the following table. (no explanation required)

7. LetP(x)=-x^3+4.5x^2-0.5x-6When factored,P(x)=-(x+1)(x-3/2)(x-4)

(a) State the domain.

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

(c) State the y-intercept:

(d) State the real zeros:

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

8. Let f(x) = (4x² - 4) / (x² - 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.

9. Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.

{(x + 1) / (x - 2)} - {6 / (x2 - 2x)} = 0

10. Which of the following functions is represented by the graph shown below? Explain your answer choice. Be sure to take the asymptotes into account in your explanation.

A. f(x)= x^2/(x^2- 16)

B. f(x)= 3/(x^2- 16)

C. f(x)= (x )/(x^2- 4x)

D. f(x)= 3/(x^2+ 4x)

11. For z = 4 - 3i and w = 7 -i, find z/w. That is, determine (4 - 3i)/(7 - i) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.

12. Consider the equation 5x² + 20 = 16x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show work.

13. The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 7.00x for x≥ 0, and the price-demand function, in dollars per widget, is p(x) = 45- 0.02x for 0 ≤ x ≤ 2250.

In Quiz 2, problem #10, we saw that the profit function for this scenario is P(x) = - 0.02x² + 38.00x - 5250.

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

Does the parabola open up or down? __________

(b) Find the vertex of the profit function P(x) using algebra. Show algebraic work.

(c) State the maximum profit and the number of widgets which yield that maximum profit:

The maximum profit is _______________ when ____________ widgets are produced and sold.

(d) Determine the price to charge per widget in order to maximize profit.

(e) Find and interpret the break-even points. Show algebraic work.

Part 2

Solve the following equation analytically:

1. 2^4x = 8
2. 3^(x-1) = 27
3. 5^2x-1 = 125
4. 4^2x = 1/2
5. 8^x = 1/128
6. 2^{(x^3-x)} = 1
7. 3^7x = 81^4-2x
8. 9 · 3^7x = (1/9)^2x
9. 3^2x = 5
10. 5^-x = 2