Key Features of 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. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0.

Front

What is a 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 function is undefined.

Front

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

Back

To find the vertical asymptote, set the denominator equal to zero and solve for x.

Front

What is the significance of the degrees of the polynomials in rational functions?

Back

The degrees of the polynomials determine the behavior of the function, including the location of asymptotes and the end behavior of the graph.

Front

What happens to the graph of a rational function as x approaches infinity?

Back

The graph approaches the horizontal asymptote, which indicates the value that the function approaches.

Front

What is the horizontal asymptote of the function f(x) = 4x - 16 / (x^2 - 16)?

Back

y = 0.

Front

What are the asymptotes of the function f(x) = (x^2 - 9x + 20) / (4x^2 - 12x - 40)?

Back

Vertical asymptotes at x = 2 and x = -2, and a horizontal asymptote at y = 1.