Let's break down the question based on the graph provided:

a. Domain of the function

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

• From the graph, the function exists from $x = -3$ to $x = 6$. Therefore, the domain is: $\boxed{[-3, 6]}$

b. Range of the function

The range is the set of all possible output values (y-values) that the function can take.

• From the graph, the function’s y-values range from $y = -3$ to $y = 4$. Therefore, the range is: $\boxed{[-3, 4]}$

c. X-intercepts

The x-intercept is the point where the function crosses the x-axis ($y = 0$).

• From the graph, the function crosses the x-axis at $x = 3$. Thus, the x-intercept is: $\boxed{(3, 0)}$

d. Y-intercept

The y-intercept is the point where the function crosses the y-axis ($x = 0$).

• From the graph, the y-intercept occurs at $(0, 3)$. Thus, the y-intercept is: $\boxed{(0, 3)}$

e. Function values

You are asked to find specific function values, $f(-1)$ and $f(5)$:

• At $x = -1$, from the graph, $f(-1) = 4$. So, $f(-1) = \boxed{4}$.
• At $x = 5$, from the graph, $f(5) = -2$. So, $f(5) = \boxed{-2}$.

Let me know if you would like more details or have any questions!

Here are 5 related questions to expand your understanding:

1. How do you determine the slope of a linear function from a graph?
2. What is the general method to find intercepts of a function?
3. How do you find the range of a function algebraically if the function is not given graphically?
4. Can a function have more than one x-intercept or y-intercept?
5. What is the difference between domain and range in the context of functions?

Tip:

When analyzing a graph, always check for points of discontinuity, where the function may not be defined for some x-values. This affects the domain!