Question

What is the difference quotient of the function g(x) = 4^x

Answer 1

Answer:

First choice

Step-by-step explanation:

The difference quotient in general is  $\frac{g(x+h)-g(x)}{h}$. To get an expression for  $g(x+h)$, replace  x  with x + h.

For this question,

$\frac{4^{x+h}-4^x}{h}=\frac{4^x\cdot4^h-4^x}{h}$

Factor  $4^x$ out of the numerator.

$\frac{4^x(4^h-1)}{h}$