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Rational Functions Graphing Quiz

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#1

Which of the following is the graph of a rational function?

Hyperbola
Explanation

A hyperbola is the graph of a rational function.

#2

What is the vertical asymptote of the function f(x) = 1 / (x - 2)?

x = 2
Explanation

Vertical asymptote occurs at x = 2.

#3

What is the behavior of the rational function f(x) = 1 / x as x approaches infinity?

The function approaches 0 from the positive side.
Explanation

Function approaches 0 from the positive side.

#4

Which of the following is NOT a factor affecting the graph of a rational function?

Constant term
Explanation

Constant term doesn't affect the graph.

#5

What is the behavior of the rational function f(x) = (2x^3 - 5x^2 + 3x) / (x^2 - 4x + 3) as x approaches 3?

The function approaches positive infinity.
Explanation

Function approaches positive infinity.

#6

What is the horizontal asymptote of the function f(x) = (3x^2 + 2) / (2x^2 - 1)?

y = 3/2
Explanation

Horizontal asymptote is y = 3/2.

#7

What does the behavior of the rational function f(x) = (x^2 - 4) / (x - 2) near x = 2 indicate?

There is a hole at x = 2
Explanation

Indicates a hole at x = 2.

#8

What is the domain of the function f(x) = 3 / (x^2 - 4x + 4)?

All real numbers except x = 4
Explanation

Domain excludes x = 4.

#9

What transformation does the function f(x) = (x + 3) / (x - 2) undergo compared to the function g(x) = 1 / x?

Horizontal shift
Explanation

Undergoes a horizontal shift.

#10

What is the slant asymptote of the function f(x) = (x^3 - 2x^2 + 5) / (x - 2)?

y = x^2 - 4x + 9
Explanation

Slant asymptote is y = x^2 - 4x + 9.

#11

What is the slant asymptote of the function f(x) = (2x^2 + 3x - 1) / (x - 1)?

y = 2x + 3
Explanation

Slant asymptote is y = 2x + 3.

#12

Which of the following rational functions has a slant asymptote?

f(x) = (x^2 + 3x + 2) / (x + 1)
Explanation

f(x) = (x^2 + 3x + 2) / (x + 1) has a slant asymptote.

#13

What is the behavior of the rational function f(x) = (x^2 - 3x + 2) / (x - 1) as x approaches infinity?

The function approaches positive infinity.
Explanation

Function approaches positive infinity.

#14

What is the horizontal asymptote of the function f(x) = (2x^3 + x^2 - 1) / (3x^3 + 4x + 5)?

y = 2/3
Explanation

Horizontal asymptote is y = 2/3.

#15

What is the slant asymptote of the function f(x) = (2x^3 + 3x^2 - 1) / (x^2 + 2)?

y = 2x + 3
Explanation

Slant asymptote is y = 2x + 3.

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