Question

The function f(x) = - 2x + m.
Determine the number m when f(−3) = 3f(0)

I'm not really sure how to do this one to find m in this scenario. Would it involve using y = mx+b? How is this determined?

Answer 1

yes, f(x) = -2x + m sure looks like y = mx + b

f(-3) = -2(-3) + m = 6 + m
f(0) = -2(0) + m = m
but we are told that f(-3) = 3f(0), so
6+m = 3m
6 = 2m
m = 3

check: then f(x) = -2x + 3
f(-3) = 6+3 = 9
f(0) = 3
is 9 three times as large as 3 ? Yes, so it looks like we got it