Absolute Value and Step Functions Homework Answer Key

Absolute Value and Step Functions — Common Core Algebra I Homework1. Consider f(x) = |x + 3| only on -6 ≤ x ≤ 2. a. Evaluate f(-5) and f(2). b. Complete the table for x = -6, -5, -4, -3, -2, -1, 0, 1, 2 and graph the function. c. On which interval is f(x) always increasing? (1) -6 < x < -3 (2) -2 < x < 1 (3) -4 < x < 0 (4) -5 < x < 2 d. State the range on this domain.2. Are |x - 5| and |x| - 5 equivalent? Give evidence.3. Graph each step function: a. f(x) = -4 for -5 ≤ x < 0, and f(x) = 4 for 0 ≤ x ≤ 5. b. g(x) = 10 for 0 ≤ x < 4, g(x) = 7 for 4 ≤ x < 8, and g(x) = 4 for 8 ≤ x ≤ 12.4. The postage graph has four horizontal steps: 0.50 dollars for 0 < x < 1, 0.70 dollars for 1 ≤ x < 2, 0.90 dollars for 2 ≤ x < 3, and 1.15 dollars for 3 ≤ x < 4, where x is weight in ounces. a. What is the charge for 1.5 ounces? b. What is the charge for exactly 3.0 ounces? c. Write the piecewise function. d. Why is 0.50 ≤ y ≤ 1.15 not the range?