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Module 3 Quiz

Polynomial & Rational Functions

Quiz Information

This quiz has 15 multiple-choice questions covering all topics from Module 3. You need 70% (11 out of 15 correct) to pass.

Time: No time limit | Attempts: Unlimited | Passing: 70%

Question 1

What is the degree of f(x) = 4x³ - 2x⁵ + x² - 7?

A. 3
B. 5
C. 2
D. 7

Question 2

For f(x) = 3x⁴ - 5x² + 2x - 1, what is the end behavior as x approaches positive infinity?

A. f(x) approaches negative infinity
B. f(x) approaches positive infinity
C. f(x) approaches 0
D. f(x) approaches 3

Question 3

If a polynomial has a zero at x = 2 with multiplicity 3, how does the graph behave at x = 2?

A. The graph touches but does not cross the x-axis
B. The graph crosses the x-axis
C. The graph has a vertical asymptote
D. The graph has a hole

Question 4

Factor completely: x³ + 8

A. (x + 2)(x² - 2x + 4)
B. (x + 2)(x² + 2x + 4)
C. (x + 2)³
D. Cannot be factored

Question 5

Factor by grouping: 2x³ + 4x² - 3x - 6

A. (2x² - 3)(x + 2)
B. (2x² + 3)(x - 2)
C. (x + 2)(2x² - 3)
D. (x - 2)(2x² + 3)

Question 6

What are the potential rational zeros of f(x) = 3x³ - 4x² + 8 according to the Rational Root Theorem?

A. ±1, ±2, ±4, ±8
B. ±1, ±3, ±1/3
C. ±1, ±2, ±4, ±8, ±1/3, ±2/3, ±4/3, ±8/3
D. ±1, ±2, ±3, ±4, ±6, ±8

Question 7

What is the domain of f(x) = (x + 2)/(x² - 16)?

A. All real numbers except x = 4
B. All real numbers except x = -4 and x = 4
C. All real numbers except x = -2
D. All real numbers

Question 8

Find the vertical asymptotes of g(x) = (x - 1)/(x² - 5x + 6)

A. x = 2 and x = 3
B. x = 3 only
C. x = 2 only
D. x = 1

Question 9

What is the horizontal asymptote of h(x) = (2x² + 3x - 1)/(4x² - 5)?

A. y = 0
B. y = 1/2
C. y = 2
D. No horizontal asymptote

Question 10

Where is the hole in the graph of f(x) = (x² - 9)/(x² + x - 12)?

A. x = 3
B. x = -3
C. x = 4
D. No hole

Question 11

Solve: (x - 3)(x + 2) > 0

A. -2 < x < 3
B. x < -2 or x > 3
C. x > 3
D. All real numbers

Question 12

Solve: x² - 4 ≤ 0

A. x ≤ -2 or x ≥ 2
B. -2 ≤ x ≤ 2
C. x < -2 or x > 2
D. -2 < x < 2

Question 13

Solve: (x + 1)/(x - 2) ≥ 0

A. x ≤ -1 or x > 2
B. x ≤ -1 or x ≥ 2
C. -1 ≤ x < 2
D. -1 < x < 2

Question 14

Which statement is true about the function f(x) = (3x⁴ - 2x)/(x³ + 1)?

A. It has a horizontal asymptote at y = 0
B. It has a horizontal asymptote at y = 3
C. It has no horizontal asymptote
D. It has a horizontal asymptote at y = 1

Question 15

If (x + 2) is a factor of x³ + ax² - 4x - 8, what is the value of a?

A. a = -2
B. a = 2
C. a = 0
D. a = 4

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Module 3 Quiz

Quiz Information

What is the degree of f(x) = 4x3 - 2x5 + x2 - 7?

For f(x) = 3x4 - 5x2 + 2x - 1, what is the end behavior as x approaches positive infinity?

If a polynomial has a zero at x = 2 with multiplicity 3, how does the graph behave at x = 2?

Factor completely: x3 + 8

Factor by grouping: 2x3 + 4x2 - 3x - 6

What are the potential rational zeros of f(x) = 3x3 - 4x2 + 8 according to the Rational Root Theorem?

What is the domain of f(x) = (x + 2)/(x2 - 16)?

Find the vertical asymptotes of g(x) = (x - 1)/(x2 - 5x + 6)

What is the horizontal asymptote of h(x) = (2x2 + 3x - 1)/(4x2 - 5)?

Where is the hole in the graph of f(x) = (x2 - 9)/(x2 + x - 12)?