Question

What rule represents the function. (0,0)(1,0.5)(2,2)(3,4.5)(4,8)

Answer 1

look at the average rate of changes: \[
(0.5, 0.5)\\
(1.5,1.5)\\
(2.5,2.5)\\
(3.5,2.5)
\]

Answer 2

That's a sign that is probably an exponential function.

Answer 3

I would try: \[
f(x)= ab^x+c
\]Since \(f(0)=0\):\[
0=ab^0+c\implies a=-c
\]

Answer 4

So\[
f(x)=ab^x-a
\]

Answer 5

You put \(f(1)=\frac 12\)\[
\frac 12=ab^1-a\implies b=\frac 1{2a}+1
\]

Answer 6

Keep doing this and you'll get it.

Answer 7

\[
2=ab^2-a
\]

Answer 8

@meggersee Do you get it?