Let's analyze the graph and solve the given problems:

From the image of the graph and the question:

• The graph shows a V-shaped function which seems to be a piecewise linear function. Based on the visual information, let's tackle each part.

a. Domain: The domain represents all the possible $x$-values that the function can take. Since the graph extends infinitely in both directions along the x-axis, the domain appears to be all real numbers.

Domain: $(-\infty, \infty)$

b. Range: The range represents all the possible $y$-values that the function can output. The graph has a minimum point at $y = -2$, and the function increases from this point. Thus, the range will be all values greater than or equal to $-2$.

Range: $[-2, \infty)$

c. X-intercepts: The x-intercepts are the points where the function crosses the x-axis (i.e., where $y = 0$). Based on the graph, the function crosses the x-axis at $x = -8$ and $x = 4$.

X-intercepts: $x = -8, 4$

d. Y-intercept: The y-intercept is the point where the function crosses the y-axis (i.e., where $x = 0$). From the graph, this happens at $y = 2$.

Y-intercept: $y = 2$

e. Function values:

• $f(-5)$: From the graph, when $x = -5$, the corresponding $y$-value is $y = 1$.
• $f(-2)$: When $x = -2$, the corresponding $y$-value is $y = 0$.

Summary of the answers:

• a. Domain: $(-\infty, \infty)$
• b. Range: $[-2, \infty)$
• c. X-intercepts: $-8, 4$
• d. Y-intercept: $2$
• e. Function values: $f(-5) = 1$, $f(-2) = 0$

Would you like more details on any of these, or need further assistance?

Related Questions:

1. How do you determine the domain and range of a piecewise function?
2. How are the x-intercepts of a function useful in real-world applications?
3. What changes to a graph can affect the x- and y-intercepts?
4. How can you graph a function when only given its domain and range?
5. What types of functions often have V-shaped graphs?

Tip: When finding the domain of a function, always check if there are any restrictions (like division by zero or square roots of negative numbers).