NAME
DATE
6-3
PERIOD
Study Guide and Intervention
Square 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.
Example
3x - 2 . State its domain and range.
Graph y = √
2
.
Since the radicand cannot be negative, the domain of the function is 3x - 2 ≥ 0 or x ≥ −
3
2
The x-intercept is −
. The range is y ≥ 0.
3
Make a table of values and graph the function.
y
x
y
2
−
3
0
1
1
2
2
3
√7
4
2
-2
O
y = √⎯
3x - 2
2
6x
4
-2
Exercises
1. y = √2x
6
-2
y
2
O
2x
4 y = √
-2
2
-4
2
6x
4
4
8x
6
D: x ≥ 0; R: y ≥ 0
4. y = 2 √
x-3
2
O
y = -3 √⎯
x
2
-6
D: x ≥ 0; R: y ≤ 0
5. y = - √
2x - 3
D: x ≥ 0; R: y ≤ 0
6. y = √
2x + 5
y
2
2
O
2
4
6
x
-2
D: x ≥ 3; R: y ≥ 0
4
2
4
6
2
x
-2
-4
x
2
y
4 y = 2√
x-3
6
x
y = - √⎯
–
-4
y
4
-2
-8
-2
Chapter 6
√2
y
y
O
O
x
−
3. y = - 2. y = -3 √
x
y = √⎯
2x + 5
-2
y = - √⎯
2x - 3
3
; R: y ≤ 0
D: x ≥ −
2
19
2
O
4
x
-2
5
D: x ≥ -−
; R: y ≥ 0
2
Glencoe Algebra 2
Lesson 6-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Graph each function. State the domain and range.
NAME
DATE
6-3
PERIOD
Study Guide and Intervention
(continued)
Square Root Functions and Inequalities
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.
Example
2x - 1 + 2.
Graph y ≤ √
Graph the related equation y = √
2x - 1 + 2. Since the boundary
should be included, the graph should be solid.
-6
1
The domain includes values for x ≥ −
, so the graph is to the right
-4
1
of x = −
.
2
-2
y
2
y = √⎯
2x - 1 + 2
2
O
4
6
x
Exercises
Graph each inequality.
6
3. y < 3 √
2x - 1
2. y > √
x+3
1. y < 2 √x
y
y
6
y = 2√
x
4
4
2
2
y
8
y = 3 √⎯
2x - 1
6
4
2
O
-2
4
6x
-2
4
2
2
4
6x
-2
2
-4
x
6
y = 2√⎯
√
2x - 3
-2
-2
8
2
4
O
4
x
6
9. y < 2 √
2x - 1 - 4
y
y
4 y = 2 √⎯
2x - 1 - 4
y = √⎯
4x - 2 + 1
2
-2
2
-2
2
O
y = √
x+1-4
8. y ≤ √
4x - 2 + 1
y
2
4
6x
y = 3x + 1 - 2
4
2
6
-2
Chapter 6
-6
4
O
-2
4
-4
7. y ≥ √
3x + 1 - 2
6
y
O
O
-2
6x
4
6. y > 2 √
2x - 3
y
y = √⎯
3x - 4
2
O
-2
5. y ≥ √
x+1-4
y
2
x
4
-2
3x - 4
4. y < √
6
2
O
-2
O
2
4
6x
-2
2
20
4
6x
-4
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
y = √
x+3