Question

What is the function rule for g?

Answer 1

`g(x)=8(2^x)`

Explanation:

Here we are given with parent function
`f(x)=2^x` and the graph which shows that the function g(x).

We are asked to guess the function g(x).

We are given the two coordinates on g(x)

(0,8) and (2,32)

Hence for x = 0 , g(x)= 8

And for x=2, g(x)= 32

Let us say that the translated function is represented by

`g(x)=a2^x+b`

`g(0)=a* 2^0+b`

Hence

`a * 2^0+b=8`

`a +b=8` --------------- (i)

also

`g(2)=32`

Hence

`a* 2^2+b=32`

`4a+b=32` -------------------(ii)

Subtracting (i) from (ii) we get

`3a=34`

Hence a = 8

Now putting this value of a in (i)

`8+b=8`

B=0

Hence
`g(x)=8 * 2^x +0`

`g(x)=8(2^x)`