Plz ! note: this is not multiple choice! 3. you are given the functions f(x)=2x+5, g(x)=(x-2)^x+3 , and h(x)=4^x. a) state which function is exponential. explain how you know. b) use a difference table to justify your answer to part (a) c) which function is linear and which is quadratic? d) use difference tables to justify your answer to part (c)

(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

step-by-step explanation: