Let's analyze the graph provided in the image to answer each part of the question:

a. The Function's Domain

The domain is the set of all x-values over which the function is defined. From the graph, the function starts at $x = -3$ and ends at $x = 8$. Therefore, the domain is:

$\text{Domain} = [-3, 8]$

b. The Function's Range

The range is the set of all y-values that the function can take. Observing the graph, the highest y-value is $4$ and the lowest y-value is $-2$. Thus, the range is:

$\text{Range} = [-2, 4]$

c. The X-Intercepts

The x-intercepts are points where the graph crosses the x-axis (i.e., where $y = 0$). From the graph, the function crosses the x-axis at $x = 1$ and $x = 8$. Therefore, the x-intercepts are:

$x\text{-intercepts} = (1, 0) \text{ and } (8, 0)$

d. The Y-Intercept

The y-intercept is the point where the graph crosses the y-axis (i.e., where $x = 0$). From the graph, the function crosses the y-axis at $(0, 4)$.

$y\text{-intercept} = (0, 4)$

e. Function Values $f(-1)$ and $f(5)$

To find $f(-1)$, look at the point on the graph where $x = -1$. From the graph, the y-value at $x = -1$ is $4$. Thus, $f(-1) = 4$.

To find $f(5)$, look at the point on the graph where $x = 5$. From the graph, the y-value at $x = 5$ is $-2$. Thus, $f(5) = -2$.

Final Answers

1. Domain: $[-3, 8]$
2. Range: $[-2, 4]$
3. X-Intercepts: $(1, 0)$ and $(8, 0)$
4. Y-Intercept: $(0, 4)$
5. Function Values:
   • $f(-1) = 4$
   • $f(5) = -2$

Would you like more details or have any questions about this problem? Here are some related questions you might find useful:

1. How do you find the domain and range from a graph?
2. What is the significance of x- and y-intercepts in a function?
3. How can we determine if a function is increasing or decreasing based on its graph?
4. What are some common mistakes when interpreting graphs of functions?
5. How does the slope of the graph affect the function values?

Tip: Always check if a graph has open or closed endpoints to determine the exact domain and range.