11-1 Square-Root Functions Warm Up Warm Up Lesson Presentatio n California Standar ds Preview Preview
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11-1 Square-Root Functions
Warm UpWarm Up
Lesson Presentation
California Standards
PreviewPreview
11-1 Square-Root FunctionsWarm Up
Find each square root.
1. 3.
Solve each inequality.
5. x + 5 ≥ 0
7. 0 ≤ 3x
Compare. Write <, >, or =.
9. 7 10. 3
62. 4.
6. 0 ≤ 4x – 8
8. 10 – 3x ≥ 0
12 –20 undefined
x ≥ –5 x ≥ 2
x ≥ 0
< >
11-1 Square-Root Functions
California Standards
Extension of 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.Also covered: 17.0
11-1 Square-Root Functions
square-root function
Vocabulary
11-1 Square-Root Functions
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, .
11-1 Square-Root Functions
11-1 Square-Root FunctionsAdditional Example 1A: Evaluating Square-Root Functions
Write the speed function.
Substitute 16 for x.
Simplify.= 8(4)
= 32
After an object has fallen 16 feet, its speed is 32 ft/s.
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.
11-1 Square-Root Functions
Write the speed function.Substitute 20 for x. Use a
calculator to find the square root.
Simplify.≈ 35.8
Additional Example 1B: Evaluating Square-Root Functions
After an object has fallen 20 feet, its speed is about 35.8 ft/s.
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 20 feet. Round your answer to the nearest tenth.
11-1 Square-Root Functions
Write the speed function.
Substitute 25 for x.
Simplify.
Find the speed of an object in free fall after it has fallen 25 feet.
= 8(5)
= 40
After an object has fallen 25 feet, its speed is 40 ft/s.
Check It Out! Example 1a
11-1 Square-Root FunctionsCheck It Out! Example 1b
Write the speed function.
Substitute 15 for x. Use a calculator to find the square root.
Simplify.
Find the speed of an object in free fall after it has fallen 15 feet. Round your answer to the nearest hundredth.
≈ 30.98
After an object has fallen 15 feet, its speed is about 30.98 ft/s.
11-1 Square-Root Functions
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.
11-1 Square-Root FunctionsAdditional Example 2: Finding Domain of Square-Root
Functions Find the domain of each square-root function.
x– 4 ≥ 0
x ≥ 4
The expression under the radical sign must be greater than or equal to 0.
Solve the inequality. Add 4 to both sides.
A.
x + 3 ≥ 0
x ≥ –3
The expression under the radical sign must be greater than or equal to 0.
Solve the inequality. Subtract 3 from both sides.
B.
11-1 Square-Root Functions
Check It Out! Example 2
Find the domain of .
The expression under the radical sign must be greater than or equal to 0.
Solve the inequality. Add 1 to both sides.
2x – 1 ≥ 0
2x ≥ 1
Divide both sides by 2.
11-1 Square-Root Functions
The function for is graphed at right. Notice there are no x-values to the left of 0 because the domain is x ≥ 0.
is y ≥ 0.
Remember that the symbol indicates the positive square root only. For this reason the range of
11-1 Square-Root Functions
Additional Example 3: Graphing Square-Root Functions
Graph .
Step 1 Find the domain of the function.
x ≥ 3 The expression under the radical sign must be greater than or equal to 3.
11-1 Square-Root FunctionsAdditional Example 3 Continued
Step 2 Choose x-values greater than or equal to 3 and generate ordered pairs.
Step 3 Plot the points. Then connect them with a smooth curve.
27
1.415
1 4
0 3
x
Graph .
11-1 Square-Root Functions
In Example 3, when generating ordered pairs, choose x-values that make the expression under the radical sign a perfect square.
Helpful Hint
11-1 Square-Root Functions
Check It Out! Example 3
Graph square root function.
Step 1 Find the domain of the function.
x ≥ 4 The expression under the radical sign must be greater than or equal to 4.
11-1 Square-Root FunctionsCheck It Out! Example 3 Continued
Graph
Step 2 Choose x-values greater than or equal to 4 and generate ordered pairs.
Step 3 Plot the points. Then connect them with a smooth curve.
28
1.416
1 5
0 4
x
11-1 Square-Root Functions
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.
11-1 Square-Root Functions
Lesson Quiz: Part II
5.
Graph each square-root function.
6.
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