Rational Functions

Front

What is a rational function?

Back

Front

What is a vertical asymptote?

Back

Front

What is a horizontal asymptote?

Back

Front

What is a hole in 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 that the function is undefined at that point.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

Front

How do you find horizontal asymptotes?

Back

Front

What happens when the degree of the numerator is greater than the degree of the denominator?

Back

When the degree of the numerator is greater, the rational function does not have a horizontal asymptote; it may have an oblique (slant) asymptote instead.

Front

What is the significance of the leading coefficient in rational functions?

Back

The leading coefficient of the numerator and denominator helps determine the horizontal asymptote and the end behavior of the function.

Front

What is the relationship between holes and vertical asymptotes?

Back

Holes occur at points where both the numerator and denominator are zero, while vertical asymptotes occur where only the denominator is zero.

Front

How do you identify a hole in a rational function?

Back

To identify a hole, factor both the numerator and denominator, and find common factors that cancel out.