1. 8.2 Graph Simple Rational Functions
Algebra II

2. Rational Function A function of the form
where p(x) & q(x) are polynomials and q(x)≠0.

3. Hyperbola A type of rational function.
x=0
A type of rational function.
Has 1 vertical asymptote and 1 horizontal asymptote.
Has 2 parts called branches. (blue parts) They are symmetrical.
We’ll discuss 2 different forms.
y=0

4. Hyperbola (continued)
One form:
Has 2 asymptotes: x=h (vert.) and y=k (horiz.)
Graph 2 points on either side of the vertical asymptote.
Draw the branches.

5. Ex 1: Graph State the domain & range.
Vertical Asymptote: x=1
Horizontal Asymptote: y=2
x y
Left of vert. asymp.
Right of vert. asymp.
Domain: all real #’s except 1.
Range: all real #’s except 2.

6. Hyperbola (continued)
Second form:
Vertical asymptote: Set the denominator equal to 0 and solve for x.
Horizontal asymptote:
Graph 2 points on either side of the vertical asymptote. Draw the 2 branches.

7. Ex 2: Graph State domain & range.
Vertical asymptote:
3x+3=0 (set denominator =0)
3x=-3
x= -1
Horizontal Asymptote:
x y
Domain: All real #’s except -1.
Range: All real #’s except 1/3.

8. Assignment