u(x)= 2x+8 if x>2 5x-2 if x greater than or equal u(-2)

We are given a piecewise function \( u(x) \) defined as:

\[
u(x) = 
\begin{cases} 
2x + 8 & \text{if } x > 2 \\
5x - 2 & \text{if } x \leq 2
\end{cases}
\]

We are asked to evaluate \( u(-2) \).

Since \(-2 \leq 2\), we use the second part of the function:

\[
u(x) = 5x - 2
\]

Substitute \( x = -2 \):

\[
u(-2) = 5(-2) - 2 = -10 - 2 = -12
\]

Thus, \( u(-2) = -12 \).

Would you like more details or have any further questions?

Here are 5 related questions to explore further:

1. How would the function change if \( u(x) \) were defined differently for \( x \leq 2 \)?
2. What is \( u(2) \) based on this piecewise function?
3. Can you graph this piecewise function, and what does the graph look like?
4. How does the function behave as \( x \) approaches 2 from the left and right?
5. What is the domain and range of \( u(x) \)?

**Tip:** Always check which condition applies to the given \( x \) value before substituting into a piecewise function.

u(x)= 2x+8 if x>2, 5x-2 if x ≤ 2; Find u(-2).

Learn how to evaluate a piecewise function with linear expressions. In this problem, we find u(-2) using the appropriate branch of the function: u(x) = 5x - 2 for x ≤ 2. Detailed solution included, suitable for students in Grades 8-10.

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