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Looking at the graph of \( y = f(x) \), we are tasked with finding all \( x \)-values for which \( f(x) = -4 \). This means we are looking for the points where the graph crosses the horizontal line \( y = -4 \).

From observing the graph, it crosses \( y = -4 \) at two points:

1. One point around \( x = -1 \).
2. Another point around \( x = 2 \).

Thus, the approximate \( x \)-values where \( f(x) = -4 \) are:

\[ x = -1 \quad \text{and} \quad x = 2. \]

Would you like further clarification or details?

Here are five related questions to explore this concept further:
1. How do you find where a function is equal to a specific value using its graph?
2. Can \( f(x) = -4 \) have more than two solutions for other types of graphs?
3. What is the significance of a function crossing a certain y-value multiple times?
4. How do different types of functions (linear, quadratic, etc.) behave when solving \( f(x) = c \)?
5. How can we algebraically solve for \( x \) in \( f(x) = -4 \) if the equation for the function is given?

**Tip:** When analyzing a graph, carefully observe where it crosses key horizontal lines (like \( y = 0 \), \( y = c \)) to determine important values of \( x \).

This problem involves analyzing the graph of a function to find where the function equals -4. Learn how to identify x-values that correspond to specific function values by observing the intersections of the graph with horizontal lines.

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