Question

Find an equation for the graph sketched below:

8
6
-5
f
on
N
-5-4-3-2-1
5 6
1 2 3 4 5

Answer 1

`f(x)=3^(x+1)-3`

Explanation:

The curve of the graph shows it is Exponential:
`f(x)=b^(x-h)+k`

To find b, h, and k, we need to "un-transform" the graph from
`f(x)=b^(x)`

1. h = horizontal shift/translation; k = vertical translation:

(0,1) ⇒ (-1,-2), so h = -1 and k = -3 and
`f(x)=b^(x+1)-3`

2. Given the points (-1,-2), (0,0), and (1,6), use one of them to find b:

`f(x)=b^(x+1)-3\\0=b^(0+1)-3\\0=b^(1)-3\\3=b^1\\3=b`

3. Place b, h, and k in their correct places in the function.