Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

What is a horizontal asymptote?

Back

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

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator polynomials.

Front

What is the vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the denominator is zero.

Front

How do you find the vertical asymptotes of a rational function?

Back

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

Front

What are x-intercepts?

Back

X-intercepts are points where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

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

Back

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

Front

What are y-intercepts?

Back

Y-intercepts are points where the graph of a function crosses the y-axis, meaning the input (x-value) is zero.

Front

How do you find the y-intercept of a rational function?

Back

To find the y-intercept, evaluate the function at x = 0.