Graphing Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where a rational function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you determine the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What does it mean if a rational function has a hole?

Back

A hole in a rational function occurs at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you find the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

Front

What is the significance of the degree of the numerator and denominator in rational functions?

Back

The degree of the numerator and denominator helps determine the behavior of the function, including the existence of horizontal asymptotes.

Front

What is the behavior of a rational function near its vertical asymptotes?

Back

Near vertical asymptotes, the function will approach positive or negative infinity.

Front

What is the end behavior of a rational function?

Back

End behavior describes how the function behaves as x approaches positive or negative infinity.