1. 11-1 Square-Root Functions Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

2. 11-1 Square-Root Functions Warm Up Find each square root. 1. 3. Solve each inequality. 5. x + 5 ≥ 0 7. 0 ≤ 3x Compare. Write, or =. 9. 7 10. 3 6 2. 4. 6. 0 ≤ 4x – 8 8. 10 – 3x ≥ 0 12–20undefined x ≥ –5 x ≥ 2 x ≥ 0 < >

3. 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

4. 11-1 Square-Root Functions square-root function Vocabulary

5. 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,.

6. 11-1 Square-Root Functions

7. 11-1 Square-Root Functions Additional 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.

8. 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.

9. 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

10. 11-1 Square-Root Functions Check 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. 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.

12. 11-1 Square-Root Functions Additional 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.

13. 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.

14. 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

15. 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.

16. 11-1 Square-Root Functions Additional 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 14 03 x     Graph.

17. 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

18. 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.

19. 11-1 Square-Root Functions Check 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 15 04 x    

20. 11-1 Square-Root Functions Lesson Quiz: Part I 1. Use the formula to find the radius of a circle whose area is 28 in 2. 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.

21. 11-1 Square-Root Functions Lesson Quiz: Part II 5. Graph each square-root function. 6.