Question

The graph of g(x) is a transformation of the graph of f(x)=3x .

Answer 1

`g(x) = 3^(x-2) -1`

Explanation:

The parent graph is f(x) = 3^x

When we compare the parent graph f(x) = 3^x with given graph

We can see that the given graph is shifted 2 units to the right and 1 unit down

When we shift 2 units to the right then we put x-2 in the exponent

Then when we shift 1 unit down, put -1 at the end

So function g(x) becomes
`g(x) = 3^(x-2) -1`

LEt check with given point (2,0) and (3,2)

`g(x) = 3^(x-2) -1`

(2,0)

`0 = 3^(2-2) -1`

`0=0` True

(3,2)

`2 = 3^(3-2) -1`

`2=2` True