Question

In order to write the equation for a piecewise linear function shown on a graph, what do you need to determine.

Answer 1

To write the equation of a piecewise linear function from its graph you need to determine, for each linear segment:

1. The x-interval where that segment applies (the domain piece), including whether each endpoint is included (closed dot) or excluded (open dot).
2. Two points on the segment (or one point and the slope) so you can compute the slope m = (y2−y1)/(x2−x1).
3. The y-intercept (b) or use a point to find b from y = mx + b.

Then write each piece as y = m x + b with the appropriate x-interval, joining the pieces into a single piecewise definition.

Example format:
f(x) = { m1 x + b1, for a ≤ x < c
m2 x + b2, for c ≤ x ≤ d }