1. Graphing
Rational
Functions

2. 2x
Graph f (x) =
x ­ 1
1. Find and sketch the vertical asymptote.
the place where the graph is undefined
where the denominator is zero
the graph will not cross the vertical asymptote
you can have more than one

4. 2. Find and sketch the horizontal asymptote.
you can have no more than one
if the degree of the numerator is less than
the denominator y = 0 is the asymptote
if degree of numerator is greater than the
denominator there is no horizontal asymptote
if the degrees are equal the line y = a/b is the
horizontal asymptote where a and b are the
lead coefficients.

5. 3. Find and plot the y ­ intercept by evaluating
f (0)
4. Find the x ­ intercept by solving the
numerator

6. 5. Use sign analysis to determine where
function is positive and negative.
6. Use smooth curves to complete graph.

7. 2
Graph f(x) = 2x
2
x ­ 4

9. ­ 1
Graph f(x) = 2
x + 6x + 9