Rational Functions

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical (x = a), horizontal (y = b), or oblique.

Front

Identify the vertical asymptotes of the function.

Back

Vertical asymptotes occur where the function is undefined, typically at values that make the denominator zero.

Front

What is the X-Intercept?

Back

The X-Intercept is the point where the graph crosses the X-axis, represented as (x, 0).

Front

How do you find the X-Intercept of a rational function?

Back

Set the numerator equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What does it mean if a function has no horizontal asymptote?

Back

It means that as x approaches infinity or negative infinity, the function does not approach a specific y-value.

Front

What is the significance of the leading coefficient in determining horizontal asymptotes?

Back

The leading coefficient of the numerator and denominator helps determine the horizontal asymptote when their degrees are equal.

Front

What is the relationship between vertical asymptotes and the factors of the denominator?

Back

Vertical asymptotes correspond to the values of x that make the denominator zero, indicating points where the function is undefined.

Front

How can you identify the behavior of a function near its asymptotes?

Back

Analyze the limits of the function as it approaches the asymptote values from the left and right.