Rational Function Graphs

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 the input values (x) approach 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. If the degree of the numerator is less than the degree of the denominator, the asymptote is y=0. If they are equal, divide the leading coefficients.

Front

What are x-intercepts?

Back

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

Back

A hole in a graph occurs at a point where a factor in the numerator and denominator cancels out, indicating that the function is not defined at that point.

Front

How do you identify a hole in a rational function?

Back

To identify a hole, factor both the numerator and denominator, and find common factors that cancel out.

Front

What is the significance of vertical asymptotes?

Back

Vertical asymptotes indicate values of x where the function approaches infinity or negative infinity, typically where the denominator is zero.

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.