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 is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as the input approaches a.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes are 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 line y = b that the graph of a rational function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be found by comparing the degrees of the numerator and denominator polynomials.

Front

What is a hole in a rational function?

Back

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

Front

How do you identify holes in a rational function?

Back

Holes are identified by factoring the numerator and denominator and finding common factors that cancel out.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is the significance of the degrees of the numerator and denominator?

Back

The degrees of the numerator and denominator determine the behavior of the rational function, including the existence of horizontal asymptotes.

Front

What is a slant asymptote?

Back

A slant asymptote occurs when the degree of the numerator is exactly one greater than the degree of the denominator.