Unit 6 Rational Functions Key Features

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 are vertical asymptotes?

Back

Vertical asymptotes are lines that a graph approaches but never touches or crosses, occurring where the denominator of a rational function is zero.

Front

How do you find vertical asymptotes of a rational function?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

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 determine horizontal asymptotes for rational functions?

Back

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

Front

What is the significance of holes in a rational function?

Back

Holes occur in a rational function when a factor cancels out from both the numerator and denominator, indicating a point where the function is undefined.

Front

What is the domain of a rational function?

Back

The domain of a rational function includes all real numbers except where the denominator 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 the y-intercept of a rational function?

Back

The y-intercept is found by evaluating the function at x=0, provided the denominator is not zero.

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, often determined by the leading terms of the numerator and denominator.