Question 1

Which of the following graphs is most likely a rational function?

Accepted Answer

A curve with two branches and a horizontal asymptote.

Answer

A circle centered at the origin.

Answer

A zigzagging line with no asymptotes.

Answer

A parabola opening downwards.

Question 2

Which of the following values of x is not part of the table of the rational function f(x)=3/x−1?

Accepted Answer

x=1

Answer

x=3

Answer

x=2

Answer

x=0

Question 3

Why does a rational function exhibit a vertical asymptote on its graph?

Accepted Answer

The denominator equals zero at certain points, making the function undefined.

Answer

The numerator and denominator are both zero at the same point.

Answer

The numerator is constant while the denominator equals zero at certain points.

Answer

The function has no terms that create discontinuities.

Question 4

A table of values for f(x)=5/x+3 shows values increasing without bound as x approaches -3. What does this suggest about the graph?

Accepted Answer

There is a vertical asymptote at x=−3.

Answer

There is a horizontal asymptote at y=5.

Answer

The graph intersects the y-axis at y=−3.

Answer

The function has no vertical asymptote.

Question 5

What behavior does the graph of a rational function exhibit near a vertical asymptote?

Accepted Answer

The graph increases or decreases without bound.

Answer

The graph intersects the asymptote at least once.

Answer

The graph levels off near the asymptote.

Answer

The graph approaches zero from both sides.

Question 6

The domain of a rational function excludes values where:

Accepted Answer

The denominator equals zero.

Answer

The function has a positive slope.

Answer

The numerator is zero.

Answer

The graph does not cross the x-axis.

Question 7

For the rational function f(x)=1/x^2−25, which values must be excluded from the domain?

Accepted Answer

x=5 and x=−5

Answer

x=0

Answer

All values of x are included.

Answer

x=25

Question 8

For f(x)=1/x^2−4x, which values must be excluded from the domain?

Accepted Answer

x=2 and x=−2

Answer

x=2 and x=0

Answer

x=4 and x=−4

Answer

x=4 and x=0

Question 9

For the rational function f(x)=1/x−6, which value must be excluded from the domain?

Accepted Answer

x=6

Answer

x=3

Answer

x=0

Answer

x=−6

Question 10

For f(x)=1/x+8, which value must be excluded from the domain?

Accepted Answer

x=−8

Answer

x=0

Answer

x=8

Answer

x=4

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