1. Graph Rational Functions
3.6
Graph Rational Functions
Vocabulary
A rational function has a rule given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0.
Rational
Function
A line that a graph approaches more and more closely.
Asymptote

2. Graph Rational Functions
3.6
Graph Rational Functions
Example 1
The graph of y = 2/x is a vertical ______________________________ of the graph of y = 1/x .
stretch

3. Graph Rational Functions
3.6
Graph Rational Functions
Example 2
The graph of y = -1/4x is a vertical __________ with a reflection in the ________ of the graph of y = 1/x .
shrink
x-axis
Note that the graph could also be viewed as being reflected in the ________ .
y-axis

4. Graph Rational Functions
3.6
Graph Rational Functions
Checkpoint. Complete the following exercise.
Compare the graph of
with the graph of
The graph is a vertical stretch
With a reflection in the x-axis of the graph of

5. Graph Rational Functions
3.6
Graph Rational Functions
The graph has the following characteristics:
If |a| > 1, the graph is a vertical ________ of the graph of
stretch
If 0 < |a| < 1, the graph is a vertical ________ of the graph of
shrink
If a < 0, the graph is a reflection in the ________ of the graph of
x-axis
The horizontal asymptote is y = __. k
The vertical asymptote is x = __. h
The domain of the function is all real numbers except x = __. h
The range of the function is all real numbers except y = __. k

6. Graph Rational Functions
3.6
Graph Rational Functions
Example 5
Step 1
Identify the asymptote of the graph. 15 9 3
The vertical asymptote is x = __. 3
The horizontal asymptote is y = __. 4
Step 2
Plot several points on each side of the ________ asymptote.
vertical
Step 3
Graph two branches that pass through the plotted points and approach the ____________.
asymptote

7. Graph Rational Functions
3.6
Graph Rational Functions
Checkpoint. Complete the following exercise. 9 3 -3

8. Graph Rational Functions
3.6
Graph Rational Functions