Question

A piecewise function g(x) is represented by the graph.


Which functions represent a piece of the function? Select three options.

g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = + 1, –2 ≤ x < 1

Answer 1

The three pieces are:

- g(x) = −2, x < −2
- g(x) = x + 1, −2 ≤ x < 1
- g(x) = −2x + 6, x ≥ 1

Reason: The left horizontal segment is y = −2 for x < −2. The middle slanted segment gives g(0)=1 and g(−2)=−1, which matches y = x+1 on −2 ≤ x < 1. The right segment includes x = 1 and gives g(1)=4, matching y = −2x + 6 for x ≥ 1. The other candidate formulas give incorrect values/slopes on those intervals.