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The problem asks for specific values based on the graph of the function \( f(x) \). Let's break it down:

### a) \( f(-6) \)
To find \( f(-6) \), we look at the value of the function when \( x = -6 \) on the graph. From the graph, we see that the function at \( x = -6 \) is at \( y = 0 \), so:
\[
f(-6) = 0
\]

### b) \( f(1) \)
To find \( f(1) \), locate the point on the graph where \( x = 1 \). From the graph, it shows that at \( x = 1 \), the function value is \( y = -4 \), so:
\[
f(1) = -4
\]

### c) Values of \( x \in D_f \) such that \( f(x) = -4 \)
We need to find where the graph of \( f(x) \) equals \( -4 \). This occurs at:
- \( x = 1 \) (as already seen for \( f(1) \)).
- \( x = 0 \), since the graph also crosses \( y = -4 \) at this point.

Thus, the values of \( x \) such that \( f(x) = -4 \) are:
\[
x = 0 \text{ and } x = 1
\]

### d) Values of \( x \in D_f \) such that \( f(x) = 2 \)
Finally, we need to find where \( f(x) = 2 \). The graph shows that \( f(x) = 2 \) at two points:
- \( x = 3 \)
- \( x = -3 \)

Thus, the values of \( x \) such that \( f(x) = 2 \) are:
\[
x = -3 \text{ and } x = 3
\]

### Summary of Answers:
- \( f(-6) = 0 \)
- \( f(1) = -4 \)
- \( x = 0 \text{ and } x = 1 \) for \( f(x) = -4 \)
- \( x = -3 \text{ and } x = 3 \) for \( f(x) = 2 \)

Do you want more details or have any questions?

Here are five related questions:
1. How do we determine the domain and range of a function from a graph?
2. Can we find the intervals where the function is increasing or decreasing from this graph?
3. What are the local maxima and minima of this function based on the graph?
4. How do we calculate the slope of the function at specific points?
5. Can this function be described as continuous or piecewise continuous?

**Tip:** When analyzing a graph, always look for key points like intercepts, peaks, and valleys to gather information about the function's behavior.

Con base en la gráfica, determine: f(-6), f(1) y los valores x ∈ D_f tales que f(x) = -4 y f(x) = 2.

Learn how to evaluate function values like f(-6) and f(1) and find the x-values for f(x) = -4 and f(x) = 2 using a graphical representation. Suitable for students in Grades 10-12.

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