6.5 - Graph Square Root and Cube Root Functions
Miss. Gomero
December 30, 2014
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Introduction
OBJECTIVE: To learn how to graph square root and cube root
functions and their transformations.
By the end of this lesson, you should know how to graph functions
such as . . .
p
y =3 x +7 3
p
y =33x 1+2
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
The Square Root and Cube Root Functions
Recall that y =
p
x and y =
p
3
x are examples or radical functions.
p
p
x and y = 3 x, respectively
p
p
The transformations are: y = a x h + k and y = a 3 x h + k,
respectively. To graph, simply pick numbers with nice square roots
or nice cube roots.
Transformations of y =
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Example 1
p
Graph y = 2 x, and state the domain and range. Compare the
p
graph with the graph of y = x.
y
Domain:
Range:
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Example 2
p
Graph y = 12 3 x, and state the domain and range. Compare the
p
graph with the graph of y = 3 x.
y
Domain:
Range:
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Example 3 - Mtd. 1
p
Graph y = 3 x + 2
4, and state the domain and range.
y
Domain:
Range:
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Example 3 - Mtd. 2
p
Graph y = 3 x + 2
4, and state the domain and range.
y
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Example 4 - Mtd. 1
Graph y =
p
23x
2 + 3, and state the domain and range.
y
Domain:
Range:
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Example 4 - Mtd. 2
Graph y =
p
23x
2 + 3, and state the domain and range.
y
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Practice 1
Graph y =
p
2 x + 1 + 3, and state the domain and range.
y
Domain:
Range:
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Practice 2
Graph y =
p
3
x +2
3, and state the domain and range.
y
Domain:
Range:
x
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions
Homework
p. 449 #3, 6, 9, 11, 12, 16, 21, 22, 25, 27, 29, 32, 33, 34.
Miss. Gomero
6.5 - Graph Square Root and Cube Root Functions