Copyri
ght
© G
lencoe/M
cG
raw
-Hill
, a
div
isio
n o
f T
he
McG
raw
-Hill
Co
mp
an
ies,
Inc.
Less
on
6-3
NAME DATE PERIOD
PDF Pass
Chapter 6 19 Glencoe Algebra 2
6-3 Study Guide and InterventionSquare Root Functions and Inequalities
Square Root Functions A function that contains the square root of a variable expression is a square root function. The domain of a square root function is those values for which the radicand is greater than or equal to 0.
Graph y = √ ��� 3x - 2 . State its domain and range.
Since the radicand cannot be negative, the domain of the function is 3x - 2 ≥ 0 or x ≥ 2 −
3 .
The x-intercept is 2 −
3 . The range is y ≥ 0.
Make a table of values and graph the function.
ExercisesGraph each function. State the domain and range.
1. y = √
�
2x 2. y = -3 √
�
x 3. y = - √
�
x −
2
4. y = 2 √
���
x - 3 5. y = - √
���
2x - 3 6. y = √ ���
2x + 5
x
y
O
y = -√��⎯2x - 3
-2
-4
2 4
2
6
x
y
O
y = √��⎯2x + 5
2
2
4
4-2
-2
x
y
O
y = -√⎯x–2
2
2
4 6
-2
-4
x
y
O
y = √��⎯3x - 2
2
2
4
4 6-2
-2
x
y
O
y = √�2x
2
2
4
6
4 6-2
-2
x
y
O
y = -3√⎯x
2 4 6 8
-2
-4
-6
-8
x
y
O
y = 2√��x - 3
2
2
4
4 6
-2
Example
x y
2 −
3 0
1 1
2 2
3 √ �
7
D: x ≥ 0; R: y ≥ 0 D: x ≥ 0; R: y ≤ 0 D: x ≥ 0; R: y ≤ 0
D: x ≥ 3; R: y ≥ 0 D: x ≥ 3 −
2 ; R: y ≤ 0 D: x ≥ -
5 −
2 ; R: y ≥ 0
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Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pa
nie
s, In
c.
NAME DATE PERIOD
PDF Pass
Chapter 6 20 Glencoe Algebra 2
Square Root Inequalities A square root inequality is an inequality that contains the square root of a variable expression. Use what you know about graphing square root functions and graphing inequalities to graph square root inequalities.
Graph y ≤ √ ��� 2x - 1 + 2.
Graph the related equation y = √ ��� 2x - 1 + 2. Since the boundary should be included, the graph should be solid.
The domain includes values for x ≥ 1 −
2 , so the graph is to the right
of x = 1 −
2 .
ExercisesGraph each inequality.
1. y < 2 √ �
x 2. y > √ ��� x + 3 3. y < 3 √ ��� 2x - 1
4. y < √ ��� 3x - 4 5. y ≥ √ ��� x + 1 - 4 6. y > 2 √ ��� 2x - 3
7. y ≥ √ ��� 3x + 1 - 2 8. y ≤ √ ��� 4x - 2 + 1 9. y < 2 √ ��� 2x - 1 - 4
x
y
O
y = 3x + 1 - 22
2
4
6
4 6-2
-2
x
y
O
y = 2√�x
2
2
4
6
4 6-2
-2
x
y
O
y = √��⎯2x - 1 + 2
2 4 6
-2
-4
-6
x
y
O
y = √��x + 3
2
2
4
6
4-2
-2x
y
O 2 4 6-2
2
4
6
8y = 3√��⎯2x - 1
x
y
O
y = √��⎯3x - 4
2 4 6-2
-2
2
4
6
x
y
O
y = √��x + 1 - 4
2
2
4
4 6
-2
-4x
y
O
y = 2√��⎯2x - 3
2 4 6
-2
-4
-6
√��
x
y
O
y = √��⎯4x - 2 + 1
-2 2 4 6
2
4
6
8
xO
y = 2√��⎯2x - 1 - 4
-2
-2
-4
2 4 6
2
4y
Study Guide and Intervention (continued)
Square Root Functions and Inequalities
6-3
Example
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