f(x) { 2×²-7, if 5<x≤10 { -x-4, if x≤5

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

\[
f(x) = 
\begin{cases} 
2x^2 - 7 & \text{if } 5 < x \leq 10 \\
-x - 4 & \text{if } x \leq 5 
\end{cases}
\]

To find \( f(-2) \), we need to determine which part of the piecewise function applies to \( x = -2 \).

Since \( -2 \) is less than 5, we use the second part of the function:

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

So, \( f(-2) = -2 \).

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. What is \( f(6) \) for this function?
2. What is the value of \( f(5) \)?
3. How would the function change if the second part were \( -2x - 4 \)?
4. What are the values of \( f(x) \) at the boundaries \( x = 5 \) and \( x = 10 \)?
5. How do piecewise functions differ from standard functions?

**Tip:** When working with piecewise functions, always check which interval your input falls into before applying the function.

Understand how to evaluate the piecewise function f(x) = { 2x^2 - 7, if 5 < x ≤ 10 | -x - 4, if x ≤ 5 }. Explore detailed examples such as finding f(-2), f(6), and f(5). Suitable for high school students.

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