9.2 Graphing Simple Rational Functions

(p. 540)

Rational Function

• A function of the form

where p(x) & q(x) are polynomials and q(x)≠0.

)(

)()(

xq

xpxf

Hyperbola

• 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.

x=0

y=0

Hyperbola (continued)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.

khx

ay

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.

dcx

baxy

c

ay

Ex: Graph State the domain & range.

21

3

x

y

Vertical Asymptote: x=1

Horizontal Asymptote: y=2

x y

-5 1.5

-2 1

0 -1

4 3Domain: all real #’s except 1.

Range: all real #’s except 2.

Left of vert.

asymp.

Right of vert.

asymp.

Ex: GraphState domain & range.Vertical asymptote:3x+3=0 (set denominator =0)

3x=-3

x= -1

Horizontal Asymptote:

c

ay

3

1y

x y

-3 .83

-2 1.33

0 -.67

2 0

Domain: All real #’s except -1.

Range: All real #’s except 1/3.

33

2

x

xy

Assignment