1. Graphing Rational Functions
Objectives:
1. Be able to identify the parent function for a rational.
Be able list the characteristic of a rational function.
Be able to graph rational functions in general form.
Be able to graph rational functions in polynomial form.
Critical Vocabulary:
Parent function, Rational Function, Asymptote

2. I. The Parent Function
Parent Functions:
This function will have a vertical asymptote at x = 0.
This function will have a horizontal asymptote at y = 0.
This function will be a hyperbola (which consists of 2 symmetrical parts called branches.
Domain: All Real #; except x ≠ 0
Range: All Real #; except y ≠ 0

3. II. The Rational Function
Parent Functions:
a: Determines the size and direction
If a is positive the graph will be in sections 1 and 3.
If a is negative the graph will be in sections 2 and 4.
lal > 1: Hyperbolas change slower
lal < 1: Hyperbolas change quicker
h: horizontal shift
(Vertical Asymptote: x = #)
K: Vertical Shift
(Horizontal Asymptote: y = #)

4. III. Graphing a Rational Function (General Form)
Example 1: Graph
1st: List the Characteristics:
Hyperbolas in S1 and S3
Slow Change
VA: x = -2
HA: y = -3
2nd: Graph your asymptotes
3rd: Find Two more points x y 1 -5 -2 -4
D: All Real #; except x ≠ -2
R: All Real #; except y ≠ -3
4th: Find the Domain and Range

5. III. Graphing a Rational Function (General Form)
Example 2: Graph
1st: List the Characteristics:
Hyperbolas in S2 and S4
Slow Change
VA: x = 1
HA: y = 3
2nd: Graph your asymptotes
3rd: Find Two more points x y 5 -3 2 4
D: All Real #; except x ≠ 1
R: All Real #; except y ≠ 3
4th: Find the Domain and Range

6. Page 561 #12, 13, 19, 21
List the Characteristics
Graph (show table)
Find Domain and Range

7. Graphing Rational Functions
Objectives:
1. Be able to identify the parent function for a rational.
Be able list the characteristic of a rational function.
Be able to graph rational functions in general form.
Be able to graph rational functions in polynomial form.
Critical Vocabulary:
Parent function, Rational Function, Asymptote
Warm Up: Graph the following:

8. IV. Graphing a Rational Function (Polynomial Form)
Example 1: Graph
1st: Find (and graph) your asymptotes
VA: Place where the function is und.
x - 3 = 0
x = 3
HA: Leading co-efficient of numerator
divided by the leading co-efficient
of the denominator.
y = 2
3rd: Find Two more points x y 4 2 9 -5
D: All Real #; except x ≠ 3
R: All Real #; except y ≠ 2
4th: Find the Domain and Range

9. IV. Graphing a Rational Function (Polynomial Form)
Example 2: Graph
1st: Find (and graph) your asymptotes
VA: Place where the function is und.
x + 2 = 0
x = -2
HA: Leading co-efficient of numerator
divided by the leading co-efficient
of the denominator.
y = 3
3rd: Find Two more points x y -4 -3 9
D: All Real #; except x ≠ -2
R: All Real #; except y ≠ 3
4th: Find the Domain and Range

10. Page 562 #27, 28, 30
(3 problems)