(a) h(x) is exponential. This is obvious from its form 4^x (x in the exponent) and as 4^x=4*4*...*4 x times revealing the constant factor 4 between terms in a progression.
(b)
x h(x)
0 1 x4
1 4 x4
2 16 x4
3 64 x4
and so on
We observe factor 4 in each step --> function is exponential
(c) f(x) is linear and potentially g(x). In your question i see g(x)=(x-2)^x+3 which is super exponential. But I suspect it is a typo and the function should be quadratic: g(x)=(x-2)^2+3. If so the answer is f(x) is linear and g(x) is quadratic.
(d) i am assuming that g(x) is quadratic (see my comment to (c))
x f(x) diff g(x) diff second diff
0 5 +2 7 -3 +2
1 7 +2 4 -1 +2
2 9 +2 3 +1
3 11 +2 4
f(x) shows constant difference -> linear
g(x) shows constant *second* difference and shows same value for multiple x (1 and 3) --> sign of a quadratic
Let me know if you need more detail
