Analyzing Graphs of Rational Functions

Front

What are x-intercepts in a graph?

Back

The x-intercepts are the points where the graph crosses the x-axis, meaning the value of y is zero.

Front

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

Back

Set the numerator of the rational function equal to zero and solve for x.

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 find vertical asymptotes in a rational function?

Back

Set the denominator of the rational function equal to zero and solve for x.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the graph approaches as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is a hole in a graph of a rational function?

Back

A hole occurs at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you find the hole in a rational function?

Back

Factor the numerator and denominator, cancel the common factors, and set the canceled factor equal to zero.

Front

What is the domain of a rational function?

Back

The domain is the set of all real numbers except where the denominator is zero.

Front

What is the range of a rational function?

Back

The range is the set of all possible output values (y-values) of the function, often excluding values that correspond to horizontal asymptotes.