https://file.aiquickdraw.com/mathbot/file/1725940294670n13s5b2z.jpg

We are given the piecewise function \( f(x) \):

\[
f(x) = 
\begin{cases} 
x^2 & \text{if } x < 0 \\
-1 & \text{if } x = 0 \\
2x + 2 & \text{if } x > 0 
\end{cases}
\]

We need to evaluate:

(a) \( f(-2) \)

Since \( -2 < 0 \), we use the first case of the piecewise function:

\[
f(-2) = (-2)^2 = 4
\]

Thus, \( f(-2) = 4 \).

Would you like to proceed with parts (b) and (c)? Feel free to ask for more details. 

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Here are some related questions to deepen your understanding:

1. What is \( f(-1) \) based on the same function?
2. How would you find \( f(2) \)?
3. What happens if you substitute \( x = 0.5 \)?
4. Can you explain how piecewise functions are used in real-life scenarios?
5. What would \( f(-5) \) equal based on this function?

**Tip:** When working with piecewise functions, always check which condition your value of \( x \) falls under before proceeding.

If f(x) is defined as follows, find (a) f(-2), (b) f(0), and (c) f(3).

Learn how to solve the piecewise function f(x) with different conditions for x. This problem involves evaluating the function at f(-2), f(0), and f(3) using quadratic and linear equations.

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