https://file.aiquickdraw.com/mathbot/file/172685884428197bacp0q.jpg

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).

Use the graph to determine the function's domain, range, intercepts, and specific values.

A detailed analysis of a piecewise function's graph, including how to find its domain, range, intercepts, and specific function values. This problem helps students understand the graphical interpretation of functions and is ideal for middle school students in Grades 7-8.

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