https://file.aiquickdraw.com/mathbot/file/17264437398883rr6jfkt.jpg

The question asks to evaluate \( f(-2) \) for the given piecewise function:

\[
f(x) = \begin{cases} 
2 - 3(x - 1) & \text{if } x \leq -1 \\
5 + x^2 & \text{if } x > -1 
\end{cases}
\]

Since \( -2 \leq -1 \), we use the first case of the function:

\[
f(x) = 2 - 3(x - 1)
\]

Now substitute \( x = -2 \):

\[
f(-2) = 2 - 3(-2 - 1)
\]
\[
f(-2) = 2 - 3(-3)
\]
\[
f(-2) = 2 + 9 = 11
\]

Thus, \( f(-2) = 11 \).

Let me know if you'd like more details or if you have any questions!

### Related Questions:
1. How do you handle piecewise functions when evaluating limits?
2. Can you explain how to graph a piecewise function like this one?
3. What is the domain and range of this piecewise function?
4. How do you differentiate a piecewise function?
5. Can the function given be continuous? If so, at which points?

**Tip:** Always check which condition of a piecewise function applies before substituting values.

Evaluate f(-2) if f(x) = { 2 - 3(x - 1) if x ≤ -1, 5 + x^2 if x > -1 }

Learn how to evaluate the piecewise function f(x) where f(x) = { 2 - 3(x - 1) if x ≤ -1, 5 + x^2 if x > -1 } by substituting -2 into the equation. This step-by-step guide focuses on solving the problem by using substitution and algebraic simplification.

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