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11-1 Square-Root Functions 11-2 Radical Expressions

Warm Ups. Preview. 11-1 Square-Root Functions 11-2 Radical Expressions 11-3 Adding and Subtracting Radical Expressions 11-4 Multiplying and Dividing Radical Expressions 11-5 Solving Radical Equations 11-6 Geometric Sequences 11-7 Exponential Functions

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11-1 Square-Root Functions 11-2 Radical Expressions

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  1. Warm Ups Preview 11-1 Square-Root Functions 11-2 Radical Expressions 11-3 Adding and SubtractingRadical Expressions 11-4 Multiplying and Dividing Radical Expressions 11-5 Solving Radical Equations 11-6 Geometric Sequences 11-7 Exponential Functions 11-8 Exponential Growth and Decay 11-9 Linear, Quadratic, and Exponential Models

  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 4. 2. 12 –20 undefined 6 x ≥ –5 x ≥ 2 6. 0 ≤ 4x – 8 8. 10 – 3x ≥ 0 x ≥ 0 < >

  3. 11-2Radical Expressions Warm Up Identify the perfect square in each set. 1. 45 81 27 1112. 156 99 8 25 3. 256 84 12 1000 4. 35 216 196 72 Write each number as a product of prime numbers. 5. 366. 64 7. 196 8. 24 81 25 196 256

  4. 11-3Adding and Subtracting Radical Expressions Warm Up Simplify each expression. 1. 14x + 15y – 12y + x 2. 9xy + 2xy – 8xy 3. –3(a + b) + Simplify. All variables represent nonnegative numbers. 4. 5. 6. 15x + 3y 3xy –3a – b + 10

  5. 11-4Multiplying and Dividing Radical Expressions Warm Up Simplify each expression. 1. 2. 3. 4.

  6. 11-5Solving Radical Equations Warm Up Solve each equation. 1. 3x +5 = 17 2. 4x + 1 = 2x – 3 3. 4. (x + 7)(x – 4) = 0 5. x2 – 11x + 30 = 0 6.x2 = 2x + 15 4 –2 35 –7, 4 6, 5 5, –3

  7. 11-6Geometric Sequences Warm Up Find the value of each expression. 1. 25 32 2. 2–5 3. –34 –81 4. (–3)4 81 5. (0.2)3 6. 7(–4)2 0.008 112 7. 8. 12(–0.4)3 –0.768

  8. 11-7Exponential Functions Warm Up Simplify each expression. Round to the nearest whole number if necessary. 625 1. 32 9 2. 54 3. 2(3)3 54 4. 54 5. –5(2)5 6. –160 –32 7. 100(0.5)2 8. 3000(0.95)8 1990 25

  9. 11-8Exponential Growth and Decay Warm Up Simplify each expression. 1. (4 + 0.05)2 3. 4. The first term of a geometric sequence is 3 and the common ratio is 2. What is the 5th term of the sequence? 5. The function f(x) = 2(4)x models an insect population after x days. What is the population after 3 days? 2. 25(1 + 0.02)3 16.4025 26.5302 1.0075 48 128 insects

  10. 11-9Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24). The population of a town is decreasing at a rate of 1.8% per year. In 1990, there were 4600 people. 2. Write an exponential decay function to model this situation. 3. Find the population in 2010. y = 4600(0.982)t 3199

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