M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
2.2 Square Root of a Function.
Lesson 2
Investigation: Comparing a Function and
its Square Root.
Let's see if we can determine how a function
and the square root of the function are related.
and
Consider the graph of
Graph both functions on the same grid.
y
8
-3
7
6
-2
5
4
-1
3
2
0
1
­5
­4
­3
­2
­1
0
­1
x
1
2
3
4
5
1
2
­2
­3
3
­4
1. What are coordinates of the points where the graphs intersect? What are those points called?
Why do you think they are they called this?
2. State the domain and range of each of the functions.
Aug 15­9:17 PM
1
M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
Do the graphs have the same domain?
Does the function
exist
where
? Why not?
What are the restrictions on the variable?
Solve the equation
Where is
. Does your solution satisfy restrictions on the variable?
? Where is
? Where is
undefined?
Sep 19­9:39 PM
2
M301.U2.L2 Square Root of a Function.notebook
Example 1:
Given
September 25, 2012
.
and
, graph the functions
a. Compare the two functions.
y
8
7
6
5
-2
-1
0
1
1.5
4
3
2
1
x
­5
­4
­3
­2
­1
0
­1
1
2
3
­2
State the domain and ranges of the functions.
Invariant points occur at
How could you determine the domain and range algebraically?
Aug 15­10:40 PM
3
M301.U2.L2 Square Root of a Function.notebook
Your Turn: Given
September 25, 2012
.
and
, graph the functions
a. Compare the two functions.
y
8
7
6
5
4
3
2
1
­5 ­4 ­3 ­2 ­1
0
­1
x
1
2
3
4
5
6
7
8
­2
State the domain and ranges of the functions.
­3
Invariant points occur at
Aug 15­10:40 PM
4
M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
and
Summary: Relative Locations of
Value of
Relative
location of
Graph of
The graph of The graphs
of
is undefined and
intersect on
the x-axis.
The graph
of
is above the
graph of
The graph of
intersects
the graph of
The graph
of
is below the
graph of
Sep 19­11:23 PM
5
M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
and
Compare the Domain and Ranges of
Example 2: Using technology, identify and compare the domain and ranges of the
following pairs of functions.
a.
and
Domain:
Range:
Domain:
Range:
b.
and
Domain:
Range:
Domain:
Range:
c.
and
Domain:
Range:
Domain:
Range:
Aug 15­10:40 PM
6
M301.U2.L2 Square Root of a Function.notebook
a.
September 25, 2012
b.
c.
Sep 19­11:59 PM
7
M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
Your Turn: Identify and compare the domain and ranges of the functions.
and
Domain:
Range:
Domain:
Range:
Aug 15­10:40 PM
8
M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
Example 3: Graph the Square Root of a Function From the Graph of the Function
Using the graphs of
.
and
a.
, sketch the graphs of
and
b.
Aug 15­10:40 PM
9
M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
Your Turn: Graph the Square Root of a Function From the Graph of the Function
Using the graphs of
.
and
a.
, sketch the graphs of
and
b.
Note: Review the 'Key Ideas ' on page 85 of your text
Aug 15­10:40 PM
10
M301.U2.L2 Square Root of a Function.notebook
September 25, 2012
1. Assignment Handouts:
BLM 2-3, 'Check Your Understanding - Graphs'
or BLM 2-4, 'Square Root of a Function'.
2. Text Pages 86 - 89, Exercises # 1 - 6, 8 - 11,
13, C3, C4
Aug 16­12:54 PM
11
Attachments
Translations Assignment 1.doc
Transforming Radicals.pdf