Characteristics of 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 horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values (x) approach positive or negative infinity.

Front

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

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If they are equal, the asymptote is the ratio of the leading coefficients.

Front

What is a hole in a rational function?

Back

A hole in a rational function occurs at a value of x where both the numerator and denominator are zero, indicating that the function is undefined at that point.

Front

How do you identify the x-coordinate of a hole?

Back

To identify the x-coordinate of a hole, factor both the numerator and denominator and find the common factors. The x-value that makes the common factor zero is the x-coordinate of the hole.

Front

What does it mean for a rational function to be undefined?

Back

A rational function is undefined at values of x that make the denominator equal to zero.

Front

What is the vertical asymptote of a rational function?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input values (x) approach a certain value, typically where the denominator is zero.

Front

How do you find the vertical asymptote of a rational function?

Back

To find the vertical asymptote, set the denominator equal to zero and solve for x.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient of the numerator determines the end behavior of the rational function as x approaches infinity or negative infinity.

Front

What is the process for simplifying a rational function?

Back

To simplify a rational function, factor both the numerator and denominator and cancel any common factors.