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

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

Back

To find the y-intercept, set x = 0 in the function and solve for y.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

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

Back

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

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes for rational functions?

Back

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What does it mean if a rational function has no vertical asymptotes?

Back

If a rational function has no vertical asymptotes, it means the denominator does not have any real roots.

Front

What is the significance of the y-intercept in a rational function?

Back

The y-intercept indicates the point where the graph of the function crosses the y-axis.

Front

How can you identify holes in the graph of a rational function?

Back

Holes occur at values of x that make both the numerator and denominator zero; these points are not included in the function.

Front

What is the end behavior of a rational function?

Back

The end behavior describes how the function behaves as x approaches positive or negative infinity.