Section 13.4
Graphing and Combining
Square Root Functions
Copyright © 2011 Pearson Education, Inc.
Graphing Square Root Functions
Horizontal Translation
Example
Compare the graph of g  x   x  3 with the graph
of f  x   x.
Solution
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 2
Graphing Square Root Functions
Horizontal Translation
Properties
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 3
Graphing Square Root Functions
Horizontal Translation
Example
If a is a large positive number, then the graph of
.g  x   a x  h  k rises more quickly than the graph
of y  x  h  k . If a is a positive number near
zero, then the graph rises more slowly.
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 4
Graphing Square Root Functions
Three-Step Method for Graphing a Square Root Function
Example
Process
To sketch the graph of f  x   a x  h  k , where
a ≠ 0,
1. Sketch the graph of y  a x.
2. Translate the graph sketched in step 1 to the right
by h units if h > 0 and to the left by |h| units if
h < 0.
3. Translate the graph sketched in step 2 up by k
units if k > 0 and down by |k| units if k < 0.
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 5
Graphing Square Root Functions
Graphing a Square Root Function
Example
Sketch the graph of g  x   2 x  4  1. Find the
domain and range of g.
Solution
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 6
Graphing Square Root Functions
Graphing a Square Root Function
Solution
Example
Continued
Domain:
Range:
y ≤ -1
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 7
Performing Operations with Square Root Functions
Performing Operations with a Square Root Function
Example
Let f  x   2 x  3 and g  x   5 x  4. Find an
equation of the following functions.
Solution
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 8
Performing Operations with Square Root Functions
Performing Operations with a Square Root Function
Solution
Example
Continued
Let
equation of the following functions.
Find an
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 9
Performing Operations with Square Root Functions
Performing Operations with a Square Root Function
Solution Continued
Let
equation of the following functions.
Find an
Copyright © 2011 Pearson Education, Inc.
Section 13.4
Lehmann, Elementary and Intermediate Algebra, 1ed
Slide 10