4-3 Attributes and Transformations of Rational Functions

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where the function is undefined, typically where the denominator of a rational function equals zero.

Front

What is the domain of a rational function?

Back

The domain of a rational function 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 of a rational function is the set of all real numbers except for any horizontal asymptotes.

Front

What does it mean for a function to have 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 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 the parent function of rational functions?

Back

The parent function of rational functions is f(x) = 1/x.

Front

What transformation occurs when a function is shifted right by 3 units?

Back

The transformation is represented as f(x) = f(x - 3).

Front

What transformation occurs when a function is shifted up by 2 units?

Back

The transformation is represented as f(x) = f(x) + 2.

Front

What is the effect of multiplying a rational function by a negative number?

Back

Multiplying a rational function by a negative number reflects the graph across the x-axis.

Front

How do you determine the horizontal asymptote of a rational function?

Back

To determine the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.