7.6: Graphing Square Root & Cube Root Functions
[Algebra 2 (Y)]
HCPS III:
• Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL
RELATIONSHIPS: Understand various types of patterns and functional relationships.
• Benchmark MA.AII.9.3: Use the properties of many types of functions (e.g.,
polynomial, step, absolute value, step, exponential, and logarithmic) to identify the function’s
graph.
• Benchmark MA.AII.9.7: Determine the domain and range of a relation given a graph or
a set of points.
Goal: Graph square root and cube root functions.
Graphs of Square Root and Cube Root Functions
The graphs of the square root function y = a x where a > 0 and the cube root
3
function y = a x where a > 0 are shown.
SQUARE ROOT FUNCTION
!
!
CUBE ROOT FUNCTION
!
!
y = a3 x
y= a x
!
!
The domain of y = a x is x " 0 .
The domain and range of y = a3 x are all real
numbers.
The range is y " 0 when a > 0 .
!
!
!
!
!
Example 1: Graph a Square Root Function
a.) Graph y = "2 x . Then state its domain and range.
!
1
b.) Graph y = 2 x . Then state its domain and range.
!
Example 2: Graph a Cube Root Function
33
y
=
x . Then state its domain and range.
a.) Graph
2
!
3
b.) Graph y = "3 x . Then state its domain and range.
!
Graphs of Radical Functions
3
To graph y = a x " h + k or y = a x " h + k , follow these steps:
!
Step 1: Sketch the graph of y = a x or y = a3 x .
Step 2: Determine
the values of h and k .
!
Step 3: Translate the graph h units horizontally and k units vertically. See
the table below
! to determine
! the direction of the translation.
Value of!h
Positive
Translate right
!
Negative
Translate left
!
Value of k
!
Positive
Negative
Translate up
Translate down
Example 3: Graph a Square Root Function
a.) Graph y =
!
x "1 . Then state its domain and range.
b.) Graph y =
x + 2 . Then state its domain and range.
!
Example 4: Graph a Cube Root Function
3
a.) Graph y = x + 1 + 2 . Then state its domain and range.
!
3
b.) Graph y = x "1 " 2 . Then state its domain and range.
!
3
c.) Graph y = x + 2 "1 . Then state its domain and range.
!