Added on:
Mar 30, 2025
User Prompt
Sketch the Graph
Draw three pieces:
For -5 ≤ x < 2: f(x) = 2 - x (straight line, decreasing)
For 2 ≤ x ≤ 5: f(x) = x - 2 (straight line, increasing)
For x < -5 or x > 5: f(x) = (1/16)x² - (1/4)x + 1 (quadratic curve)
Label:
Intercepts (0, 2) and (2, 0)
Critical point at x = 2
Boundary points at x = -5 and x = 5
Annotate behavior:
Decreasing on [-5, 2), increasing on [2, 5]
Non-differentiable at x = -5, 2, 5 (sharp turns)