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 –

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Warm Up Find each square root Solve each inequality. 5. x + 5 ≥ ≤ 3x Compare. Write <, >, or = ≤ 4x – – 3x ≥ 0 12–20 undefined x ≥ –5 x ≥ 2 x ≥ 0 < >

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

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,.

Example 1: 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.

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) = 24 After an object has fallen 25 feet, its speed is 24 ft/s. Now You Try…

Write the speed function. Substitute 20 for x. Use a calculator to find the square root. Simplify. ≈ 35.8 Example 2: Evaluating Square-Root Functions Using a Calculator 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.

Now You Try… 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. ≈ After an object has fallen 15 feet, its speed is about ft/s.

Example 2: Find The Domain 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. 2 x – 1 ≥ 0 2 x ≥ 1 Divide both sides by 2.

Find the domain of each square-root function. x ≥ 0 x ≥

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 Example 3: Graphing xy

Graphing Square-Root Functions Graph. Step 1 Find the domain of the function. x ≥ 3 x – 3 ≥ 0 Step 2 Choose x -values greater than or equal to 3 and generate ordered pairs xy

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

In Example 3, when generating ordered pairs, choose x-values that make the expression under the radical sign a perfect square. Helpful Hint

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 ≥

Lesson Quiz: Part II 5. Graph each square-root function. 6.