Question

Write a rule for the linear function in the table.

x f(x)
–4 16
0 0
4 –16
8 –32



A. f(x) = –4x


B. f(x) = x + 16


C. f(x) = 4x


D. f(x) = x

Answer 1

A. f(x) = –4x

Answer 2

Ok. We're told that f(x) is linear, so it will be a polynomial of order 1. In other words, a line in the form of y=mx+b.

Finding b is easy as we have f(0). Since f(0)=0, then 0=m0+b, which implies that b is 0.

Then using any other set of points (say x=-4) we can find m:\[f(-4)=m(-4)+0=16\]\[\rightarrow m=-4\]So\[f(x)=-4x\]

Answer 3

thank you