1. 3.6 Warm Up
Find the initial point, state the domain & range, and compare to the parent function f(x) = √x.
y = 3√x – 1
y = -1/2√x
y = - √(x-1) + 2
y = 3√-x

2. 3.6 Graph Rational Functions

3. Vocabulary:
A rational function has a rule given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0.
An asymptote is a line that a graph approaches more and more closely.

4. a x 1 x
EXAMPLE 1
Compare graph of y = with graph of y = 1 –2 x
is a
The graph of a.
b. The graph of
y = 3x
vertical stretch with a reflection in the x - axis of the graph of
vertical shrink of the graph of = y 1 x y = x 1

5. Compare to parent function:1. 2. 3.

6. Steps to graph: Identify and sketch asymptotes.
Make a t-chart w/ three points on either side of the vertical asymptote.
Plot points & draw graph.
Compare to the parent function.
Identify domain and range.

7. Graph y = k 1 x
EXAMPLE 2
Graph y = and identify its domain and range. Compare the graph with the graph of y = . 1 x

8. Graph y = 1
x – h
EXAMPLE 3
Graph y = and identify its domain and range. Compare the graph with the graph of y = . 1
x– 2 x

10. Graph y = k a
x – h
EXAMPLE 4
Identify the domain and range and compare with the parent function.
Graph y = – 3. 2
x + 1

11. GUIDED PRACTICE
for Example 4
Identify the domain and range and compare with the parent function. 5.
Graph y = 4
x – 5

12. GUIDED PRACTICE
for Example 4 6.
For which function is the domain all real numbers except –3 and the range all real numbers except 7 ?
A. y = 2
x – 3
B. y = – 7. 2
x – 3
C. y = 2
x + 3
D. y = – 7. 2
x + 3
ANSWER
C. y = 2
x + 3

13. Determine the asymptotes of the graph of the function.1. 2.

14. Write an equation whose graph has the given asymptotes and passes through the given point.
x = -2, y = 5; (0, -2)

15. Write an equation whose graph has the given asymptotes and passes through the given point.
2. x = -4, y = -4; (-5, 3)