Algebra 2 Notes
Section 6.5: Graph Square Root and Cube Root Functions
Objective(s):
Vocabulary:
I. Radical Function:
(See Glossary p. 1069)
II. Parent Function:
(See p. 89)
KEY CONCEPT: Parent Functions
Square Root Functions: f(x) =
x
Cube Root Functions: g(x) =
Domain:
Domain:
Range:
Range:
3
x
REVIEW: STRETCHES, SHRINKS, AND REFLECTIONS (Section 2.7)
Consider the graph of
For a  1
ya x
For a  1
If a < 0
KEY CONCEPT: Graphs of Radical Functions
To graph
Step 1:
Step 2:
or
, follow these steps:
Notes 6.5 page 2
Examples:
1. Graph the following functions and state their domain and range.
a) y  2 x
b) y 
33
x
2
2. Graph the following functions and state their domain and range.
a) y  x  2
b) y  x 1  3
c) y  3 x  1
d) y  3 x  1  4
3. Compare the graphs of the functions with their parent function. Be sure to describe whether it is a vertical stretch or shrink,
the horizontal and vertical shifts, and if there is a reflection.
a) y  3 x  8
b) y 
1
x 5 2
2
c) y  2
3
x 1  4
d) y  5 3 x  4
Algebra 2 Notes
Objective(s):
Section 6.5: Graph Square Root and Cube Root Functions
To be able to graph square root and cube root functions.
Vocabulary:
I. Radical Function:
A function that contains a radical with a variable in its radicand.
(See Glossary p. 1069)
II. Parent Function:
The most basic function in a family.
(See p. 89)
KEY CONCEPT: Parent Functions
Square Root Functions: f(x) =
x
Cube Root Functions: g(x) =
3
Domain:
x>0
Domain:
all real numbers
Range:
y>0
Range:
all real numbers
x
REVIEW: STRETCHES, SHRINKS, AND REFLECTIONS (Section 2.7)
Consider the graph of
For a  1
ya x
For a  1
Vertical Stretch
Vertical Shrink
(graph is narrower)
(graph is wider)
If a < 0
Reflection over the x-axis
KEY CONCEPT: Graphs of Radical Functions
To graph
y  a x h  k
or
y  a 3 x h  k
, follow these steps:
Step 1:
Sketch the graph of y  a x or y  a 3 x .
Step 2:
Translate the graph horizontally h units and vertically k units.
Notes 6.5 page 2
Examples:
1. Graph the following functions and state their domain and range.
a) y  2 x
b) y 
33
x
2
Domain:
x>0
Domain:
all real numbers
Range:
y<0
Range:
all real numbers
2. Graph the following functions and state their domain and range.
a) y  x  2
b) y  x 1  3
Domain:
x>0
Domain:
x>1
Range:
y>2
Range:
y>3
c) y  3 x  1
d) y  3 x  1  4
Domain:
all real numbers
Domain:
all real numbers
Range:
all real numbers
Range:
all real numbers
3. Compare the graphs of the functions with their parent function. Be sure to describe whether it is a vertical stretch or shrink,
the horizontal and vertical shifts, and if there is a reflection.
a) y  3 x  8
Vertical Stretch
Vertical Shift of 8
b) y 
1
x 5 2
2
Vertical Shrink
Horizontal Shift of 5
Vertical Shift of -2
c) y  2
3
x 1  4
Vertical Stretch
Horizontal Shift of -1
Vertical Shift of -4
Reflection over x-axis
d) y  5 3 x  4
Vertical Stretch
Horizontal Shift of 4