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Name: Date: Algebra 2 Review Problems Review: Solving Equations and Inequalities Types of problems: Methods you’ll need to use: solving an equation finding a function’s zeros solving an inequality that has a number on one side (such as f(x) ≤ #) solving a double inequality (such as # ≤ f(x) ≤ #) algebraic solving (when the functions involved are linear) graphical solving using intersections graphical solving using zeros 1. A graph of a function f(x) is given. Answer these questions about f(x). If an answer involves a non-whole number, make a reasonable estimate. The whole graph is shown. No arrows at ends! a. What is the domain of f(x)? b. Solve f(x) = 1. c. Find the zeros of f(x). d. Solve -4 < f(x) < –2. e. Solve f x 0 2. Answer the following questions involving function f(x) = 12 ( x 4) 3 . This is a line, so add arrows to the end! graph of f(x) = 12 ( x 4) 3 a. Solve graphically: 1 ( x 4) 3 1 . 2 b. Solve graphically: 12 ( x 4) 3 1 . c. Solve graphically: 1 12 ( x 4) 3 2 . d. Find the zeros of f(x) = 12 ( x 4) 3 graphically. Name: Date: Algebra 2 Review Problems 3. g(x) is below. Questions may require estimating. g(x) continues down on both sides. a. Find the domain of g(x) . b. Find the range of g(x) . c. Find the zero(s) of g(x) . d. Find g(2) . e. Solve g(x) 4 . f. Solve g(x) 2 . g. Solve g(x) 4 h. Solve the equation g(x) 7 . 4. Answer the following questions about the function f (x) given at the right. You may assume that the graphcontinues infinitely far in both directions. a. Find the domain of f(x). b. Find the range of f(x). c. Find the zero of f(x). d. Solve f(x) = –4. e. Solve f(x) ≥ –2. f. Solve f(x) < 2. g. Solve 0 < f(x) < 2. Name: Date: Algebra 2 Review Problems 5. a. Solve graphically on your calculator: 3x + 1 = –x + 5. (Use INTERSECTIONS.) b. Check your answers to part a by solving the same problems algebraically. 3x + 1 = –x + 5 6. a. Solve graphically on your calculator using INTERSECTIONS: 4 2x 2 6 . (Draw the calculator graph that you use.) Note that you will need two horizontal lines. b. Solve algebraically: 4 2x 2 6 . Name: Date: 7. Algebra 2 Review Problems Solve graphically on your calculator by finding a zero. (Hint: you will need to get 0 on one side of = first) (Draw the calculator graph you used.) 0.7x + 3 > 3.2x – 5.5 8. Solve algebraically: a. –4 < – 13 x + 2 < 7 b. 4 ≤ –2(x + 3) + 1 ≤ 13 Name: Date: Algebra 2 Review Problems ANSWERS: 1. a. –5 ≤ x ≤ 6 b. x = 0, x ≈ 2.6, x ≈ 5.4 c. x = –1, x = 3, x = 5. d. –5 ≤ x ≤ 3. e. –1 < x < 3, 5 < x ≤ 6. 2. a. x = 4 b. x < 4 c. –2 < x < 4 d. x = 2 3. a. All real numbers b. gx 4.2 c. x = 1.5, x = –2.5 f. x 2 or x 1 g. 1 x 0 4. a/b All real numbers c. x 2 d. 2 e. –1, 0 h. No solution d. x 4 e. x 1 5. a. x = 1 b. x = 1 6. a/b. –4 ≤ x ≤ 1. 7. a. –2.5x + 8.5 > 0 b. 8. a. 15 x 18 b. 9 x 4.5 x = 3.4 f. x 5 g. –5 < x < –2