1. For the piecewise function f(x) = {-2x - 1, x ≤ 2; -x + 4, x > 2}:
- When x ≤ 2, use f(x) = -2x - 1. For example:
- At x = 0: f(0) = -2(0) - 1 = -1
- At x = 1: f(1) = -2(1) - 1 = -3
- At x = 2: f(2) = -2(2) - 1 = -5
- When x > 2, use f(x) = -x + 4. For example:
- At x = 3: f(3) = -3 + 4 = 1
- At x = 4: f(4) = -4 + 4 = 0
- The graph shows a line with slope -2 for x ≤ 2 and a line with slope -1 for x > 2. There is an open circle at (2, 2) on the second piece and a closed circle at (2, -5) on the first piece.
2. For the piecewise function f(x) = {-4, x < -2; x - 2, -2 ≤ x < 2; -2x + 4, x ≥ 2}:
- When x < -2, f(x) = -4 (a horizontal line).
- When -2 ≤ x < 2, f(x) = x - 2 (a line with slope 1). For example:
- At x = -2: f(-2) = -2 - 2 = -4
- At x = 0: f(0) = 0 - 2 = -2
- At x = 1: f(1) = 1 - 2 = -1
- When x ≥ 2, f(x) = -2x + 4 (a line with slope -2). For example:
- At x = 2: f(2) = -2(2) + 4 = 0
- At x = 3: f(3) = -2(3) + 4 = -2
- At x = 4: f(4) = -2(4) + 4 = -4
- The graph should show a horizontal line at y = -4 for x < -2, a line segment from (-2, -4) to (2, 0) with open circle at (2, 0), and a ray starting at (2, 0) going down with slope -2.
Parent Tip: Review the logic above to help your child master the concept of piecewise functions worksheet kuta.
