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The function \( f(x) \) is defined piecewise as follows:

\[
f(x) = 
\begin{cases} 
x^2 & \text{if } x < 0 \\
3 & \text{if } x = 0 \\
2x + 4 & \text{if } x > 0
\end{cases}
\]

Now, we will evaluate the given points:

### (a) \( f(-4) \):
Since \( -4 < 0 \), we use the rule \( f(x) = x^2 \). Therefore:
\[
f(-4) = (-4)^2 = 16
\]

### (b) \( f(0) \):
Since \( x = 0 \), we use the rule \( f(x) = 3 \). Therefore:
\[
f(0) = 3
\]

### (c) \( f(2) \):
Since \( 2 > 0 \), we use the rule \( f(x) = 2x + 4 \). Therefore:
\[
f(2) = 2(2) + 4 = 4 + 4 = 8
\]

Thus, the answers are:
- \( f(-4) = 16 \)
- \( f(0) = 3 \)
- \( f(2) = 8 \)

Would you like more details on any part of the solution?

Here are 5 related questions to explore:

1. How would the value of \( f(x) \) change if \( f(x) = x^3 \) for \( x < 0 \)?
2. What is \( f(1.5) \) for the same function definition?
3. How do you determine whether to use \( f(x) = x^2 \) or \( f(x) = 2x + 4 \) for other negative or positive values?
4. Can you graph the piecewise function to visualize its behavior for all values of \( x \)?
5. What happens to \( f(x) \) as \( x \) approaches infinity or negative infinity?

**Tip**: In piecewise functions, always check which condition applies to the given value of \( x \) before plugging it into the function.

If f(x) is defined as follows, find (a) f(-4), (b) f(0), and (c) f(2). f(x) is defined as: f(x) = {x^2 if x < 0, 3 if x = 0, 2x + 4 if x > 0}.

Learn how to evaluate a piecewise function defined by different rules depending on the value of x. This solution covers the steps to find f(-4), f(0), and f(2) using the given piecewise definitions: x^2 for x < 0, 3 for x = 0, and 2x + 4 for x > 0. Suitable for students in Grades 9-11.

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