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

Step-by-step 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

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

(2,0)

True

(3,2)

True

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3