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6-3

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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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om

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c.

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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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