Name
LESSON
Date
Class
Reteach
11-5 Square-Root Functions
A square-root function is a function in which the independent variable is
under the square-root sign.
Square-root
functions
#
!x
Determine whether y ! 5 " ___
is a
2
square root function. Explain.
Not square-root
functions
!
!
y ! !2x " 3 y ! 2x " !3
!
y ! 4 " !!
x
y ! !4 x
Because x is under the square-root sign, this
is a square root function.
The square root of a negative number is not a real number.
Therefore, the x-values must be restricted to numbers that
make the value under the radical sign greater than or equal to 0.
#
#
Find the domain of y ! !x " 5 .
Find the domain of y ! 3 % !4x % 12 .
x " 5 is under the radical sign.
x " 5 must be greater than or equal to zero.
x"5$0
#5 _
#5
Add #5 to both sides.
_
x $ #5
4x # 12
4x # 12
zero.
4x # 12
"12
_
The domain is the set of all real numbers
greater than or equal to #5.
is under the radical sign.
must be greater than or equal to
$0
"12
_
4x $ 12
12
4x $ ___
___
4
4
x$3
Add 12 to both sides.
Divide each side by 4.
The domain is the set of all real numbers
greater than or equal to 3.
Determine whether the following are square-root functions. Explain.
no, x is not under the square-root sign.
!
1. y ! ! 8 " x
yes, x is under the square-root sign.
!
2. y ! ! 8 " x
Find the domain of each square root function.
!
3. y ! ! 5x # 8
4. y ! 6 "
8
x $ __
5
!
5. y ! !3x # 5
x$0
!
6. y ! ! 2 " x # 5 #
7. y !
x$5
!
x
__
#8
!5
x$0
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c11-5_rt.indd 38
!
!x
Process Black
38
x$0
8. y !
!
x
__
!3 " 2
x $ %6
Holt Algebra 1
12/26/05 8:27:17 AM
Name
Date
Class
Reteach
LESSON
11-5 Square-Root Functions (continued)
You can use the domain of the square-root function to help you graph.
#
Graph f " x # ! !3x % 6 .
x
Step 1: Find the domain of the function.
2
f " x # ! ! 3x % 6
0
5
3
14
6
29
9
3x # 6
"6
_
3x
$0
"6
_
$6
3x – 6 must be greater
than or equal to zero.
#
6
3x $ __
___
3
3
x$2
Y
The domain is the set of all real numbers
greater than or equal to 2.
Step 2: Choose x-values greater than or
equal to 2 to generate ordered pairs.
X
Graph each square-root function.
!
!
9. y ! !2x
x$0
Domain:
!
11. y ! ! 2x " 6
x $ %3
Domain:
Domain:
!
x $ %3
!
x
f " x # ! !2x
x
f " x # ! !x " 3
x
f " x # ! !2x " 6
0
2
8
18
32
0
2
4
6
8
%3
1
6
22
33
0
2
3
5
6
%3
%1
5
15
29
0
2
4
6
8
Y
Y
Y
X
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c11-5_rt.indd 39
!
10. y ! !x " 3
Process Black
X
X
39
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