Graphing Rational Functions

The factors in the ________________ determine the vertical asymptotes.

• numerator

• denominator

The factors in the ________________ determine the roots.

• numerator

• denominator

If the degree is higher in the numerator, the horizontal asymptote is...

• y = 0

• y = leading coefficient

• No horizontal asymptote

If the degree is higher in the denominator, the horizontal asymptote is...

• y = 0

• y = leading coefficient

• No horizontal asymptote

If the degree is the same in the numerator and denominator, the horizontal asymptote is...

• y = 0

• y = leading coefficient

• No horizontal asymptote

How do you know if the graph of a written rational function has a slant asymptote?

How do you know if the graph of a written rational function has a hole?

Describe the steps for finding the x- and y-value of the hole in a graph.

To find the y-intercept,...

• Set the factors in the numerator equal to 0.

• Set the factors in the denominator equal to 0.

• Plug 0 in for all x-values.

• Plug 0 in for the y-value.

To determine the behavior of the graph on either side of a vertical asymptote,...

• Look at the exponents in the numerator.

• Look at the exponents in the denominator.

• There's no way to know.