Graphs with Linear Parts Practice (Piecewise) - MathBitsNotebook(A1) - Free Printable

- The graph represents a piecewise function.
- For x ≤ 1, the function is a line passing through (-4, -3) and (1, 2). The slope is (2 - (-3)) / (1 - (-4)) = 5/5 = 1. Using point-slope form: y - 2 = 1(x - 1), so y = x + 1. At x = 1, it's a solid dot, so this piece includes x = 1.
- For x > 1, the function is a line passing through (1, -1) [open circle] and (3, -3). The slope is (-3 - (-1)) / (3 - 1) = (-2)/2 = -1. Using point-slope form with (1, -1): y - (-1) = -1(x - 1), so y = -x. Since the point at x=1 is open, this piece is for x > 1.
- Therefore, the piecewise function is:
f(x) = { x + 1, if x ≤ 1
{ -x, if x > 1