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The question involves analyzing the graph of \( y = f(x) \) and determining various values for \( f(x) \) based on the graph. I'll provide step-by-step help with each part shown in the image:

### Part 1 of 8
(a) **Determine \( f(-4) \):**
- The value \( f(-4) \) represents the y-coordinate of the point on the graph where \( x = -4 \). From the graph, it appears that when \( x = -4 \), the value of \( y = 0 \). Therefore:
  \[
  f(-4) = 0
  \]

### Part 2 of 8
(b) **Determine \( f(1) \):**
- Similarly, \( f(1) \) is the y-coordinate when \( x = 1 \). The graph shows that when \( x = 1 \), \( y = -1 \). Hence:
  \[
  f(1) = -1
  \]

### Part 3 of 8
(c) **Find all \( x \) for which \( f(x) = -1 \):**
- The question asks for the values of \( x \) where the function equals \( -1 \). By looking at the graph, we can see that the function intersects \( y = -1 \) at \( x = -3, 1, \) and \( 3 \). Thus:
  \[
  \text{Values of } x \text{ for which } f(x) = -1: \quad x = -3, 1, 3
  \]

### Part 4 of 8
(d) **Find all \( x \) for which \( f(x) = -4 \):**
- From the graph, we look for the points where the function equals \( -4 \). There seems to be no point on the graph where \( y = -4 \), so:
  \[
  \text{There is no } x \text{ such that } f(x) = -4.
  \]

Let me know if you need any additional details or clarification on these steps.

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Here are 5 related questions to expand on this topic:
1. What is the value of \( f(0) \) from the graph?
2. For what value(s) of \( x \) does \( f(x) = 0 \)?
3. What is the maximum value of \( f(x) \) on the graph?
4. Find all values of \( x \) where the graph has local minima.
5. How can you tell if a function is increasing or decreasing from its graph?

**Tip:** When analyzing graphs, always check the y-coordinates corresponding to the given x-values carefully, especially at intersection points.

Use the graph of y = f(x) to determine various function values, such as f(-4), f(1), and solve for x when f(x) equals certain values.

Learn how to evaluate f(x) using a graph, including determining specific values for f(-4), f(1), and finding x-values where f(x) = -1 or other values. This problem helps students practice function evaluation through graph interpretation, suitable for Grades 9-12.

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