Let's analyze the graph and answer the questions provided.

A) Domain of $f(x)$:

The domain is the set of all possible input values (x-values) for which the function is defined. Looking at the graph, the function extends infinitely to the left and right, meaning the function is defined for all real numbers except at $x = -2$, where there is a vertical asymptote.

Answer: The domain of $f(x)$ is $(-\infty, -2) \cup (-2, \infty)$.

B) Range of $f(x)$:

The range is the set of all possible output values (y-values). The function approaches negative infinity as $x$ moves left or right, but there's a lower boundary around $y = -8$ where the graph doesn't go below. The graph also approaches positive infinity at the vertical asymptote but appears to be bounded above, around $y = 8$.

Answer: The range of $f(x)$ is approximately $[-8, 8]$.

C) $x$-Intercepts:

The x-intercepts are points where the graph crosses the x-axis, i.e., where $f(x) = 0$. By observing the graph, we can see that the graph crosses the x-axis at two points: $x = -5$ and $x = 2$.

Answer: The x-intercepts are $(-5, 0)$ and $(2, 0)$.

Do you want further details or have any questions?

Here are 5 related questions for further practice:

1. What are the $y$-intercepts of $f(x)$?
2. Identify the intervals where $f(x)$ is increasing or decreasing.
3. What is the behavior of $f(x)$ near the vertical asymptote at $x = -2$?
4. Find the coordinates of the local maximum and minimum points.
5. Does the function have any symmetry (odd, even, or neither)?

Tip: When dealing with vertical asymptotes, always check for undefined values in the function's domain, which may cause discontinuities.