Rational Functions

Front

What is a rational function?

Back

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a value of x where both the numerator and denominator are zero, indicating that the function is undefined at that point.

Front

How do you find the coordinates of a hole in a rational function?

Back

To find the coordinates of a hole, factor both the numerator and denominator, cancel the common factors, and then substitute the x-value of the canceled factor into the simplified function.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a. They occur at values of x that make the denominator zero but not the numerator.

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator equal to zero and solve for x, ensuring that these x-values do not also make the numerator zero.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the function approaches as x approaches infinity or negative infinity. They describe the end behavior of the function.

Front

How do you determine horizontal asymptotes in rational functions?

Back

To determine horizontal asymptotes, compare the degrees of the numerator and denominator: If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What are x-intercepts of a rational function?

Back

X-intercepts are points where the graph of the function crosses the x-axis, found by setting the numerator equal to zero and solving for x.

Front

How do you find the x-intercepts of a rational function?

Back

To find x-intercepts, set the numerator of the rational function equal to zero and solve for x.

Front

What is the domain of a rational function?

Back

The domain of a rational function includes all real numbers except those that make the denominator zero.