Let's break down the problem step by step. The function given is:

$g(x) = -\log_4(x - 3) + 2$

Part A: Graph the function, determine the domain, range, and x-intercepts.

1. Domain:

   • The argument of the logarithm, $x - 3$, must be positive: $x - 3 > 0 \implies x > 3$ Thus, the domain is: $\boxed{(3, \infty)}$

2. Range:

   • The base function $-\log_4(x - 3)$ has a range of $(-\infty, \infty)$.
   • Adding $+2$ shifts the range vertically by 2, so the range remains: $\boxed{(-\infty, \infty)}$

3. X-Intercept:

   • To find the x-intercept, set $g(x) = 0$: $-\log_4(x - 3) + 2 = 0$ Rearrange: [ -\log_4(x - 3) = -2 \implies \log