https://file.aiquickdraw.com/mathbot/file/1728409260970dqbkcc3j.jpg

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, \( f(5) = \boxed{-2} \).

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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!

Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if there is one; e. the following function values: f(-1), f(5).

Learn how to determine the domain, range, x-intercepts, y-intercept, and specific function values from a graph. This problem includes analyzing the graph of a linear function. Suitable for students in Grades 8-10.

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