Graphing Rational Functions

Front

What is the X-Intercept?

Back

The X-Intercept is the point where the graph of a function crosses the X-axis. It occurs when y = 0.

Front

What is the Horizontal Asymptote?

Back

The Horizontal Asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

Which asymptote(s) are determined by looking at the denominator?

Back

Vertical asymptotes are determined by the values of x that make the denominator equal to zero.

Front

What are the asymptotes of the function f(x) = (x-1)/(x^2-1)?

Back

The asymptotes are x = 1 (vertical) and y = 0 (horizontal).

Front

What is the horizontal asymptote of the function f(x) = 4/(x+1)?

Back

The horizontal asymptote is y = 0.

Front

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

Back

Set the denominator equal to zero and solve for x.

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 degree of the numerator and denominator in determining horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If they are equal, the asymptote is y = leading coefficient of numerator/leading coefficient of denominator.

Front

What is a hole in a rational function?

Back

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

Front

How do you determine the end behavior of a rational function?

Back

Analyze the degrees of the numerator and denominator to predict the behavior as x approaches positive or negative infinity.