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 11-8 Exponential Growth and Decay 11-9 Linear, Quadratic, and Exponential ModelsPreview Warm Ups

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

Warm Up Identify the perfect square in each set Write each number as a product of prime numbers Radical Expressions

Warm Up Simplify each expression x + 15y – 12y + x 2. 9xy + 2xy – 8xy 3. –3(a + b) + Simplify. All variables represent nonnegative numbers x + 3y 3xy –3a – b Adding and Subtracting Radical Expressions

Warm Up Simplify each expression Multiplying and Dividing Radical Expressions

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

Warm Up Find the value of each expression –5 3. – (–3) (0.2) (–4) 2 – (–0.4) 3 – Geometric Sequences

Warm Up Simplify each expression. Round to the nearest whole number if necessary (3) –5(2) –32 – (0.5) (0.95) Exponential Functions

Warm Up Simplify each expression. 1. ( ) 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? ( ) insects 11-8 Exponential Growth and Decay

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 y = 4600(0.982) t Linear, Quadratic, and Exponential Models