https://file.aiquickdraw.com/mathbot/file/1726154753432f6nkdolm.jpg

Let's analyze the graph and answer the questions based on the provided information:

### a. The function's domain:
The graph shows a V-shaped structure, which is typical of an absolute value function. Since the graph continues indefinitely to the left and right (as indicated by the arrows), the function is defined for all real numbers.

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

### b. The function's range:
The lowest point of the graph appears to be at \( y = 0 \). The function extends upwards from there, so the range is from \( y = 0 \) to \( \infty \).

**Range**: \( [0, \infty) \)

### c. The x-intercepts, if any:
The graph crosses the x-axis at \( x = -5 \) and \( x = 5 \). These are the x-intercepts.

**X-intercepts**: \( x = -5 \) and \( x = 5 \)

### d. The y-intercept, if any:
The graph crosses the y-axis at \( y = 5 \).

**Y-intercept**: \( y = 5 \)

### e. The function values \( f(-3) \) and \( f(-1) \):
From the graph, we can estimate the function values for these x-values:
- For \( x = -3 \), the graph is at \( y = 2 \).
- For \( x = -1 \), the graph is at \( y = 4 \).

**Function values**:
- \( f(-3) = 2 \)
- \( f(-1) = 4 \)

### Summary of answers:
a. Domain: \( (-\infty, \infty) \)  
b. Range: \( [0, \infty) \)  
c. X-intercepts: \( x = -5 \) and \( x = 5 \)  
d. Y-intercept: \( y = 5 \)  
e. Function values: \( f(-3) = 2 \), \( f(-1) = 4 \)

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Do you have any further questions or would you like more details on any of the points?

Here are five follow-up questions you might find helpful:
1. How do you find the vertex of an absolute value function?
2. How can you determine the slope of the graph from this function?
3. What is the general form of an absolute value function equation?
4. How would the graph change if the function had a negative leading coefficient?
5. How would you calculate the inverse of this function?

**Tip**: To find the range of a function from a graph, look at the minimum and maximum values that the function's output (y-values) can take!

Use the graph to determine the following: a) the function's domain, b) the function's range, c) the x-intercepts, if any, d) the y-intercept, if any, e) the function values f(-3) and f(-1). Assume that the graph of the function continues its trend beyond the displayed coordinate grid.

Learn how to determine the domain, range, x-intercepts, and y-intercept of a function from its graph. Also, calculate function values at specific points. This problem covers key algebraic concepts and graph analysis suitable for students in Grades 8-10.

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