Quiz Math
1. (A) Solve the inequality x2 ≤ 7x and write the solution set in interval notation.
(no explanation required)
A. [7, ∞)
B. (-∞, 0] U [7, ∞)
C. (-∞, 7] U [0, ∞)
D. [0, 7]
(B) Solve (x + 4)/(x^(2 )+ 2x- 3) υ 0 and write the solution set in interval notation. 1B. ______
(no explanation required)
A. (-3, 1)
B. (-∞, -4] υ (-3, 1)
C. (-∞, -4]
D. [-4, 1) U (15, ∞)
2. For f (x) = x3 - 3x2 - 5, use the Intermediate Value Theorem to determine which interval must contain a zero of f. (no explanation required) 3. _______
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
3. Translate this sentence about area into a mathematical equation.
The area A of a circle is directly proportional to the square of the length r of its radius.
4. Each graph below represents a polynomial function. Complete the following table.
(Explain all answers)
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. Let P(x)=-x^3+4.5x^2-0.5x-6 When 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).
(c) State the y-intercept:
(d) State the real zeros:
(e) State which graph below is the graph of P(x).
GRAPH A. (below) GRAPH B. (below)
GRAPH C. (below) GRAPH D. (below)
6. (5 pts) Let . (no explanations 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. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
8. Which of the following functions is represented by the graph shown below? Explain your answer choice (Why). 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)= 3/(x^2+ 4x)
D. f(x)= (x )/(x^2- 4x)
9. (10 pts) For z = 4 - 3i and w = 3 - i, find z/w. That is, determine (4 - 3i)/(3 - i) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.
10. 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.