1. Graph the function f(x) = { x + 5, x < 0; 2x - 2, x ≥ 0 }.
- For x < 0: Plot the line y = x + 5. Use an open circle at (0, 5) since x=0 is not included.
- For x ≥ 0: Plot the line y = 2x - 2. Use a closed circle at (0, -2) since x=0 is included.
2. Graph the function f(x) = { -x + 2, x ≤ 0; 3x + 1, x > 0 }.
- For x ≤ 0: Plot the line y = -x + 2. Use a closed circle at (0, 2) since x=0 is included.
- For x > 0: Plot the line y = 3x + 1. Use an open circle at (0, 1) since x=0 is not included.
3. Write a piecewise function for the given graph.
- The graph shows two parts:
- A line with slope 2 passing through (0, -4) and extending to the left (x ≤ 0). Equation: y = 2x - 4.
- A horizontal line at y = 2 for x > 0.
- Piecewise function: f(x) = { 2x - 4, x ≤ 0; 2, x > 0 }.
4. Write a piecewise function for the given graph.
- The graph shows two parts:
- A line with slope 1 passing through (0, 0) and extending to the right up to x=2 (0 ≤ x ≤ 2). Equation: y = x. Use closed circles at (0,0) and (2,2).
- A horizontal line at y = -2 for x > 2.
- Piecewise function: f(x) = { x, 0 ≤ x ≤ 2; -2, x > 2 }.
Parent Tip: Review the logic above to help your child master the concept of algebra 2 piecewise function worksheet.
