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The function \( f(x) \) provided is a piecewise function defined differently based on the value of \( x \). It's given by:

1. \( f(x) = 3x - 2 \) for \( x < -2 \)
2. \( f(x) = -x \) for \( -2 \leq x < 1 \)
3. \( f(x) = x^2 - 7x \) for \( x \geq 1 \)

To evaluate \( f(x) \) for specific values of \( x \), you'll need to identify which condition the value of \( x \) satisfies and then apply the corresponding function. If you have specific values of \( x \) for which you would like to evaluate \( f(x) \), please let me know those values.

Would you like details or have any other questions? Here are some related questions we can explore:
1. What is the derivative of \( f(x) \) at a specific value?
2. How can you find the limits of \( f(x) \) as \( x \) approaches the boundaries of these intervals?
3. What is the behavior of \( f(x) \) as \( x \) approaches infinity?
4. How can you graph this piecewise function?
5. What are the critical points of \( f(x) \) for optimization problems?

Tip: When dealing with piecewise functions, it's crucial to consider boundary conditions and continuity at the points where the function definition changes.

Evaluate the piecewise function f(x), defined as:
- f(x) = 3x - 2 for x < -2
- f(x) = -x for -2 ≤ x < 1
- f(x) = x^2 - 7x for x ≥ 1

Learn how to evaluate a piecewise function defined by different formulas for distinct intervals of x. This example includes linear and quadratic functions across three segments. Suitable for high school students in grades 9-12.

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