6.5 Graph Square Root and Cube Root Functions
Date _________________
Goal  Graph square root and cube root functions.
REVIEW:
Write the expression in simplest form.
1) √
3) √
2) (25a10b16)1/2
4) Find the inverse of the function y = 4x2 + 9
PARENT FUNCTIONS FOR SQUARE ROOT AND CUBE ROOT FUNCTIONS

The parent function for the family of square root functions is f(x) = x .
Graph the parent function ( )
√
The domain of x =
The range of y =

The parent function for the family of cube root functions is g(x) =
Graph the parent function ( )
√
The domain of x =
The range of y =
3
x
Example 1
Graph a square root function
Graph y = 2 x , and state the domain and range. Compare the graph with the graph of y = x
Step 1) T-Chart Use x’s : 0,1,4,9
Step 2) Ask what is being done to
the parent function?
Step 3) Do the same to the y’s in
the t-chart
Step 4) Graph x’s and the new y’s
Domain:
Range:
Graph a cube root function
Graph y = 
1
2
3
x , and state the domain and range.
Step 1) T-Chart Use x’s : -8,-1,0,1,8
Step 2) Ask what is being done to the
parent function?
Step 3) Do the same to the y’s in the
t-chart
Step 4) Graph x’s and the new y’s
Domain:
Range:
SUPERSTAR CHECK! Graph the function. Then state the domain and range.
1. y = 2
3
x
2. y = 2 x
Domain:
Range:
Homework: Page449 3-8,10-15
Domain:
Range:
6.5 Day 2 Graphing Square and Cube Roots
Date__________________
REVIEW:
Write the expression in simplest form
2. √
1) √
Perform the indicated operation and state the domain. f(x) = 2x + 9 and g(x) = 3x – 1
3. f(x) – g(x)
4. f(f(x))
Find the inverse of the function
6. f(x) = x3 + 5
NOTES:
GRAPHS OF RADICAL FUNCTIONS
To graph y = a x  h + k or y =a 3 x  h + k, follow these steps:
a and (h,k) h effects x
a and k effects y
Graph a translated square root function
Graph y = 3 x  1 + 2. Then state the domain and range.
Solution
Step 1) T-Chart Use x’s : 0,1,4,9
Step 2) Ask what is being done to the
parent function? a =
h=
k=
Step 3) Do the same to the x’s and the
y’s in the t-chart
Step 4) Graph x’s and the new y’s
Domain:
Range:
5. f(x)·g(x)
Example 4
Graph a translated cube root function
Graph y = 2 3 x  3 2. Then state the domain and range.
Step 1) T-Chart Use x’s : -8,-1,0,1,8
Step 2) Ask what is being done to the
parent function? a = h =
k=
Step 3) Do the same to the x’s and y’s in
the t-chart
Step
4) Graph x’s and the new y’s
3
x
Domain:
Range:
SUPERSTAR CHECK! Graph the function. Then state the domain and range.
1. y = 
2. y = 3
1
2
3
x3 +2
x+2
Homework P. 449 16-24