https://file.aiquickdraw.com/mathbot/file/1725988011320pxeg5yll.jpg

Let's go over the parts one by one based on the provided graph of the function \( f(x) \):

1. **Part (a)**
   - \( f(12) = 8 \)
   - \( f(0) = -4 \)
   
2. **Part (c)**: Is \( f(4) \) positive or negative?
   - From the graph, at \( x = 4 \), the function value \( f(4) = -8 \), so it is **negative**.

3. **Part (d)**: Is \( f(-6) \) positive or negative?
   - At \( x = -6 \), the function value \( f(-6) = 12 \), so it is **positive**.

4. **Part (e)**: For what value(s) of \( x \) is \( f(x) = 0 \)?
   - The points where \( f(x) = 0 \) are the x-intercepts of the graph. These points are at \( x = -12, -2, 8, 12 \).

Thus, for part (e), the values of \( x \) are:
   \[
   x = -12, -2, 8, 12
   \]

Let me know if you would like further details or explanations on any part! 

Here are some related questions for further understanding:
1. How do you find the x-intercepts of a function graphically?
2. What does it mean when \( f(x) = 0 \)?
3. How would you determine whether a function is increasing or decreasing from a graph?
4. How can you tell if a function is positive or negative from its graph?
5. What does it mean when the function has multiple points where \( f(x) = 0 \)?

**Tip**: To determine if a function is positive or negative at a given point, look at whether the function lies above or below the x-axis at that point!

Use the given graph of the function f to answer parts (a)-(e).

Learn how to interpret a graph of a function to determine specific function values, positivity or negativity of points, and identify x-intercepts. Suitable for students in Grades 9-11.

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