Transcript Lesson 6.4B

Rational
Rational Functions
Functions
• How do we graph rational functions?
• How do we transform rational functions
by changing parameters?
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Algebra 2Algebra 2
Holt
Rational Functions
ax  b
The graph of a y 
cx  d
Vertical asymptotes:
has the following characteristics.
d
x
c
a
Horizontal asymptotes: y 
c
Then plot 2 points to the
left and right of the center
Holt McDougal Algebra 2
Rational Functions
Graph the function. State the domain and range.
x
1. y 
x2
 2
y 1
Vertical asymptotes: x
Horizontal asymptotes:
x
4
3
1
0
y
Domain:
2
3a l l R x   2
 1 Range:
0 a ll R y  1
Holt McDougal Algebra 2
Rational Functions
Graph the function. State the domain and range.
2x
2. y 
x4
Vertical asymptotes:
Horizontal asymptotes:
x
x 4
y2
y
Domain:

2
2
3 6 a l l R x  4
5 10 Range:
6 6 a ll R y  2
Every line worth 2
Holt McDougal Algebra 2
Rational Functions
Graph the function. State the domain and range.
x2
3. y 
x3
x  3
Vertical asymptotes:
Horizontal asymptotes:
x
y
y 1
 5 3/2
 4 2 a ll R x   3
 2 0 Range:
 1 1 / 2 a ll R y  1
Domain:
Holt McDougal Algebra 2
Rational Functions
Graph the function. State the domain and range.
x 1
4. y 
2x  3
Vertical asymptotes: x  3 / 2
Horizontal asymptotes: y  1 / 2
x
y
0 1/ 3
Domain:
0 a ll R x  3 / 2
Range:
2
32 / 3 a ll R y  1 / 2
Holt McDougal Algebra 2
Rational Functions
Graph the function. State the domain and range.
2x  6
5. y 
x4
Vertical asymptotes:
x4
Horizontal asymptotes: y  2
x
y
Domain:
2
3 0 a ll R x  4
5 4 Range:
6 3 a ll R y  3
Holt McDougal Algebra 2
Rational Functions
Graph the function. State the domain and range.
4x  8
6. y 
2x  5
Vertical asymptotes: x  2 . 5
Horizontal asymptotes: y  2
x
y
1 .3
2 0
3 4
4 2 .7
Domain:
a ll R x  2 . 5
Range:
a ll R y  2
Holt McDougal Algebra 2
Rational Functions
Lesson 6.4 Practice B
Holt McDougal Algebra 2