Use the function $g(x)$ as defined below to answer parts (a)-(d). $\begin{align*} g(x) = \begin{cases} x+6, & x<0\\ 3, & x=0\\ 6(0.5)^x, & x>0 \end{cases} \end{align*}$
a) Which of the following is an accurate sketch a graph of $g(x)$ on the interval $[-5,5]$?

A. A
B. B
C. C
D. D

A		B
C		D

b) What are the domain and range of $g(x)$?

A. Domain: $(-\infty, \infty)$, Range: $(-\infty, 0) \cup (0, 6)$
B. Domain: $(-\infty, \infty)$, Range: $(-\infty, \infty)$
C. Domain: $[-\infty, \infty]$, Range: $(-\infty, 6]$
D. Domain: $(-\infty, \infty)$, Range: $(-\infty, 6)$

c) Over what intervals is $g(x)$ increasing? Decreasing?

A. Increasing: $(-\infty, 0)$; Decreasing: $(0, \infty)$
B. Increasing: $(-\infty, 0]$; Decreasing: $(0, \infty)$
C. Increasing: $(-\infty, 6)$; Decreasing: $(6, 0)$
D. Increasing: $(-\infty, 0)$; Decreasing: $[0, \infty]$

d) State the long-run behavior of $g(x)$ as $x \to \infty$, and give the equation(s) of any horizontal asymptote(s).
Long-run behavior:

A. As $x$ goes to $\infty$, $g(x)$ approaches $\infty$.
B. As $x$ goes to $\infty$, $g(x)$ approaches $6$.
C. As $x$ goes to $\infty$, $g(x)$ approaches 0.
D. As $x$ goes to $\infty$, $g(x)$ approaches $- \infty$

Horizontal asymptote(s):
? g(x) = x =

Hint: