Question

Do all linear functions increase along their entire​ domain? Explain.
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Part 1
Choose the correct answer.
A.
​No; all linear functions fall from left to​ right, so all linear functions decrease along their entire domain.
B.
​Yes; the domain of linear functions is ​[0,infinity​), so all linear functions increase along their entire domain.
C.
​Yes; all linear functions rise from left to​ right, so all linear functions increase along their entire domain.
D.
​No; it is possible for a linear function to decrease along its entire domain or remain constant.

Answer 1

D.

A linear function has form f(x) = mx + b. If m > 0 it increases (rises left to right), if m < 0 it decreases (falls left to right), and if m = 0 it is constant. The domain of linear functions is all real numbers, so any of those behaviors can occur on the entire domain.