3.6 Graph Rational 3.6 Graph Rational Functions Functions

3.6 Graph Rational 3.6 Graph Rational Functions Functions

Part IIPart II

Remember• Rational functions have asymptotes• To find the vertical asymptote, set the

denominator = 0 and solve for x

• x-5 = 0• x=5

13

5y

x

To find horizontal asymptote

• Eliminate any term that involves an x and solve for y

• y = 3

13

5y

x

Using Asymptotes to Graph

• Draw dotted lines for asymptotes• Pick values for x based on the

asymptotes and solve for y

GUIDED PRACTICE for Examples 1, 2 and 3

Graph the function and identify its domain and range. Compare the graph with the graph of y = 1

x

ANSWER

1. y = – 4x

Domain: all real numbers except 0

Range: all real numbers except 0

The graph is a vertical stretch of y = that is then reflected in the x-axis.

1 x

GUIDED PRACTICE for Examples 1, 2 and 3

2. y = 1 x – 4

1 x

Domain: all real numbers except 0

Range: all real numbers except – 4

The graph is a vertical translation (of 4 units down) of the graph y = .

ANSWER

Graph the function and identify its domain and range. Compare the graph with the graph of y = 1

x

GUIDED PRACTICE for Examples 1, 2 and 3

3. y = 1 x + 5

1 x

Domain: all real numbers except – 5

Range: all real numbers except 0

The graph is a horizontal translation (of 5 units left) of the graph y = .

Graph the function and identify its domain and range. Compare the graph with the graph of y = 1

x

ANSWER

GUIDED PRACTICE for Examples 1, 2 and 3

y = 1 x + 3

4. Describe how the graph of is related to the graph of y = .1

x

The graph of y = is a horizontal translation (of 3 units left) of the graph of y = .

x + 31

x1

ANSWER

SOLUTION

EXAMPLE 4 Graph y = + k ax – h

Graph y = – 3.2

x + 1

GUIDED PRACTICE for Example 4

5. Graph y = + 6 4x – 5

ANSWER

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 = + 7.2x – 3 B. y = – 7.2

x – 3

C. y = + 7.2x + 3 D. y = – 7.2

x + 3

ANSWER

C. y = + 7.2x + 3