Rational Function Graphs

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

How do you find the y-intercept of a rational function?

Back

To find the y-intercept, set x = 0 in the function and solve for y.

Front

What does it mean if a rational function has a vertical asymptote?

Back

A vertical asymptote indicates that the function approaches infinity or negative infinity as it gets close to a certain x-value, where the function is undefined.

Front

How do you determine the 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 positive or negative infinity.

Front

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

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator polynomials.

Front

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

Back

The degree of the numerator and denominator helps determine the behavior of the function at infinity and the existence of horizontal asymptotes.

Front

What happens to the graph of a rational function at its vertical asymptotes?

Back

The graph will approach the vertical asymptote but will never touch or cross it.

Front

What is the relationship between the y-intercept and the function's value at x=0?

Back

The y-intercept is the value of the function when x=0, represented as (0, f(0)).

Front

What does it mean if a rational function has no y-intercept?

Back

If a rational function has no y-intercept, it means that the function is undefined at x=0.