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The screenshot you've shared seems to show a table and a piecewise function. The function \( f(x) \) is defined differently depending on the value of \( x \). Here’s a breakdown of what’s on the image:

1. For \( x < 1 \), the function is defined as \( f(x) = -2x \).
2. For \( x \geq 1 \), the function is defined as \( f(x) = x - 4 \).

The table provided shows values for both sections of the function:

- For \( x = -1 \), \( f(x) = -2(-1) = 2 \).
- For \( x = 0 \), \( f(x) = -2(0) = 0 \).
- For \( x = 1 \), \( f(x) = 1 - 4 = -3 \).

The piecewise function, therefore, switches from \( -2x \) to \( x - 4 \) at \( x = 1 \). 

If you're asking about \( f(x) = x - 4 \) in general, this is a simple linear function with a slope of 1 and a y-intercept at -4.

Do you need help graphing this or interpreting further details? Feel free to ask!

Here are 5 follow-up questions:
1. How do you determine where the piecewise function changes?
2. What is the domain of the function \( f(x) = x - 4 \)?
3. What does the slope of \( f(x) = x - 4 \) tell you about the graph’s behavior?
4. How would you graph the piecewise function on a coordinate plane?
5. Can you explain the importance of the point where the two pieces of the function meet?

**Tip:** Always check for continuity at the point where a piecewise function changes (in this case, at \( x = 1 \)).

This solution breaks down a piecewise function with two parts: f(x) = -2x for x < 1, and f(x) = x - 4 for x ≥ 1. Explore the step-by-step calculations, including points like (1, -3), and understand how linear functions behave across different domains. Suitable for students in Grades 9-12.

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