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.

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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.

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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.