Question 1

Which graph could represent a rational function?

Accepted Answer

A curve with two branches and a vertical asymptote

Answer

A semicircle

Answer

A straight line

Answer

A parabola opening upwards

Question 2

For the rational function f(x) = 1/(x + 3); which value of x is not in its table of values?

Accepted Answer

x = -2

Answer

x = 0

Answer

x = -3

Answer

x = 1

Question 3

Why might a rational function have a vertical asymptote on its graph?

Accepted Answer

The denominator of the function equals zero at certain points.

Answer

The numerator of the function equals zero at certain points.

Answer

The function has a constant term in the equation.

Answer

The graph has no points where the function is undefined.

Question 4

What does the behavior of a rational function f(x) approach as x gets close to 3 if the values show infinity?

Accepted Answer

There is a vertical asymptote at x=3.

Answer

The function has no asymptotes.

Answer

There is a vertical asymptote at x=0.

Answer

The function has a horizontal asymptote at y=3.

Question 5

What typically happens to the graph of a rational function near a vertical asymptote?

Accepted Answer

The graph increases or decreases without bound.

Answer

The graph tends to approach zero.

Answer

The graph remains constant.

Answer

The graph crosses the asymptote.

Question 6

The domain of a rational function consists of all real values of x for which:

Accepted Answer

The denominator is nonzero.

Answer

The graph is continuous.

Answer

The numerator is nonzero.

Answer

The function is zero.

Question 7

For the rational function f(x) =

\frac{1}{x^2-100}

; which value must be excluded from the domain?

Accepted Answer

x = 10

Answer

x = -10

Answer

x = 10 and x = -10

Answer

x = 0

Question 8

For the function f(x) = 1/(x - 10); which value must be excluded from the domain?

Accepted Answer

x = 10

Answer

x = -10

Answer

x = -9

Answer

x = 9

Question 9

For the rational function f(x) = 1/(x + 5), which value must be excluded from the domain?

Accepted Answer

x = -5

Answer

x = 3

Answer

x = 3

Answer

x = 5

Question 10

Given the rational function f(x) = 5x/(x^2 - x - 20), evaluate the domain.

Accepted Answer

{x ∈ ℝ | x ≠ 5 and x ≠ -4}

Answer

{x ∈ ℝ | x ≠ 4}

Answer

{x ∈ ℝ | x ≠ -5}

Answer

All real numbers

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