Graphs of Rational functions

Front

What is a rational function?

Back

Front

What is the domain of a rational function?

Back

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

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a. It occurs where the denominator of a rational function is zero.

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph of the function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes for rational functions?

Back

For rational functions, compare the degrees of the numerator and denominator: If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote. If they are equal, divide the leading coefficients.

Front

What is a hole in a graph of a rational function?

Back

A hole occurs in the graph of a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you find the coordinates of a hole?

Back

To find the coordinates of a hole, factor the numerator and denominator, cancel the common factors, and evaluate the remaining function at the x-value of the canceled factor.

Front

What transformations can occur with rational functions?

Back

Transformations of rational functions can include shifts (up, down, left, right), reflections (over the x-axis or y-axis), and stretches or compressions.

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept of a rational function is the point where the graph crosses the x-axis, found by setting the numerator equal to zero.