4.6 - Rational Functions CHeckpoint Review

Front

What is a rational function?

Back

Front

What are removable discontinuities in rational functions?

Back

Removable discontinuities, or holes, occur at values of x where both the numerator and denominator of a rational function equal zero, allowing the function to be simplified.

Front

How do you find vertical asymptotes of a rational function?

Back

Front

What is a horizontal asymptote?

Back

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

Front

How do you determine horizontal asymptotes for rational functions?

Back

1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. 2. If the degrees are equal, the horizontal asymptote is y = \frac{a}{b}, where a and b are the leading coefficients.

Front

What is the domain of a rational function?

Back

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

Front

Back

Front

What is the significance of vertical asymptotes?

Back

Vertical asymptotes indicate values of x where the function approaches infinity or negative infinity, representing points of discontinuity.

Front

Back

Since the degree of the numerator (1) is less than the degree of the denominator (2), the horizontal asymptote is y = 0.

Front

Back