Holt Algebra 1 11-5 Square-Root Functions 11-5 Square-Root Functions Holt Algebra 1 Warm Up Warm Up...

Holt Algebra 1

11-5 Square-Root Functions11-5 Square-Root Functions

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

11-5 Square-Root Functions

Warm Up

Find each square root.

1.

3.

Solve each inequality.

5. x + 5 ≥ 0

7. 0 ≤ 3x

6 2.

4.

6. 0 ≤ 4x – 8

8. 10 – 3x ≥ 0

12

–20 undefined

x ≥ –5 x ≥ 2

x ≥ 0

Holt Algebra 1


Warm Up Continued

Compare. Write <, >, or =.

9. 7

10. 3

<

>

Holt Algebra 1


Identify square-root functions and their domains and ranges.

Graph square-root functions.

Objectives

Holt Algebra 1


square-root function

Vocabulary

Holt Algebra 1


The function gives the speed in feet per second of an object in free fall after falling x feet. This function is different from others you have seen so far. It contains a variable under the square-root sign, .

Holt Algebra 1


Holt Algebra 1


Example 1A: Evaluating Square-Root Functions

Write the speed function.

Substitute 16 for x.

Simplify.

The function gives the speed in feet per second of an object in free fall after falling x feet.

Find the speed of an object in free fall after it has fallen 16 feet.

= 8(4)

= 32After an object has fallen 16 feet, its speed is 32 ft/s.

Holt Algebra 1


Write the speed function.Substitute 20 for x. Use a

calculator to find the square root.

Simplify.


Find the speed of an object in free fall after it has fallen 20 feet. Round your answer to the nearest tenth.

= 8(4.47)

≈ 35.8

Example 1B: Evaluating Square-Root Functions

After an object has fallen 20 feet, its speed is about 35.8 ft/s.

Holt Algebra 1



Substitute 25 for x.

Simplify.


Find the speed of an object in free fall after it has fallen 25 feet.

= 8(5)

= 40After an object has fallen 25 feet, its speed is 40 ft/s.

Check It Out! Example 1a

Holt Algebra 1


Check It Out! Example 1b


Substitute 15 for x. Use a calculator to find the square root.

Simplify.

The function gives the speed in feet per second of an object in free fall after falling x feet.Find the speed of an object in free fall after it has fallen 15 feet. Round your answer to the nearest hundredth.

= 8(3.87)

≈ 30.98After an object has fallen 15 feet, its speed is about 30.98 ft/s.

Holt Algebra 1


Recall that the square root of a negative number is not a real number. The domain (x-values) of a square-root function is restricted to numbers that make the value under the radical sign greater than or equal to 0.

Holt Algebra 1


Example 2A: Finding the Domain of Square-root Functions

Find the domain of the square-root function.

x– 4 ≥ 0

+ 4 + 4

x ≥ 4

The expression under the radical sign must be greater than or equal to 0.

Solve the inequality. Add 4 to both sides.

The domain is the set of all real numbers greater than or equal to 4.

Holt Algebra 1



x + 3 ≥ 0

–3 –3

x ≥ –3


Solve the inequality. Subtract 3 from both sides.

The domain is the set of all real numbers greater than or equal to –3.

Example 2B: Finding the Domain of Square-root Functions

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2x – 1 ≥ 0+1 +1

2x ≥ 1

Divide both sides by 2.

The domain is the set of all real numbers greater than or equal to .

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The expression under the radical sign must be greater than or equal to 0.3x – 5 ≥ 0

+ 5 +53x ≥ 5


Divide both sides by 3.

The domain is the set of all real numbers greater than or equal to .

Holt Algebra 1


The parent function for square-root functions, is graphed at right. Notice there are no x-values to the left of 0 because the domain is x ≥ 0.

Holt Algebra 1


If a square-root function is given in one of these forms, you can graph the parent function and translate it vertically or horizontally.

Holt Algebra 1


Example 3A: Graphing Square-Root Functions

Graph .

Graph f(x) = and then shift the graph 3 units to the right.

Since this function is in the form f(x) = , you can graph it as a horizontal translation of the graph of f(x) =

Holt Algebra 1


Example 3B: Graphing Square-Root Functions

Graph .

This is not a horizontal or vertical translation of .

Step 1 Find the domain of the function.

x ≥ 0 The expression under the radical sign must be greater than or equal to 0.


Holt Algebra 1


Example 3B Continued

Step 2 Choose x-values greater than or equal to 0 and generate ordered pairs.

Step 3 Plot the points. Then connect them with a smooth curve.

11.356

104

71

40

x

Graph .

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Graph each square root function.

Graph f(x) = and then shift the graph 2 units up.

Since this function is in the form f(x) = , you can graph it as a vertical translation of the graph of f(x) =

Holt Algebra 1



Graph each square root function.

This is not a horizontal or vertical translation of .

Step 1 Find the domain of the function.

x ≥ 0The expression under the radical sign

must be greater than or equal to 0.


Holt Algebra 1


Check It Out! Example 3b Continued

Step 2 Choose x-values greater than or equal to 0 and generate ordered pairs.

Graph .

7.896

74

51

30

x

Step 3 Plot the points. Then connect them with a smooth curve.

Holt Algebra 1


Lesson Quiz: Part I

1. Use the formula to find the radius of a circle

whose area is 28 in2. Use 3.14 for . Round your

answer to the nearest tenth of an inch.

Find the domain of each square-root function.

3.0 in.

x ≥ 0

x ≥ 5

2.

3.

4.

Holt Algebra 1


Lesson Quiz: Part II

5.

Graph each square-root function.

6.

Holt Algebra 1 11-5 Square-Root Functions 11-5 Square-Root Functions Holt Algebra 1 Warm Up Warm Up...

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