Rational Graphs Review

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided the numerator is not also zero at those points.

Front

What is a hole in a rational function?

Back

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

Front

Write the general form of a rational function.

Back

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, found by setting f(x) = 0.

Front

What is the domain of a rational function?

Back

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

Front

How do you determine the domain of the function f(x) = \frac{x^2 - 9}{x^2 + 6x + 9}?

Back

Set the denominator x^2 + 6x + 9 = 0 and solve for x to find restrictions on the domain.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote describes the behavior of the function as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes?

Back

For rational functions, compare the degrees of the numerator and denominator to determine horizontal asymptotes.