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The given piecewise-defined function is:

\[
f(x) = 
\begin{cases} 
-\frac{2}{7}x + 4 & \text{if } x < 3 \\
8x - 9 & \text{if } x \geq 3
\end{cases}
\]

We are asked to find \( f(3) \).

Since \( x = 3 \), we will use the second part of the piecewise function because it applies to \( x \geq 3 \):

\[
f(x) = 8x - 9
\]

Substitute \( x = 3 \):

\[
f(3) = 8(3) - 9 = 24 - 9 = 15
\]

Thus, \( f(3) = 15 \).

Would you like further clarification on this? Here are five related questions for further practice:

1. What is \( f(2) \) for the same function?
2. How would the function change if the condition were \( x \leq 3 \) instead of \( x \geq 3 \)?
3. What is the slope of the function \( f(x) = -\frac{2}{7}x + 4 \)?
4. If the piecewise function changed to \( f(x) = 8x - 12 \) for \( x \geq 3 \), what would \( f(3) \) be?
5. What is the domain of the piecewise function?

**Tip**: Always check the condition associated with the piecewise function to ensure you're using the correct part of the function for the given input.

Find f(3) for this piecewise-defined function.

Learn how to evaluate the piecewise-defined function f(x) for x = 3. The problem involves using different expressions for x values less than and greater than or equal to 3. Suitable for students in Grades 9-10.

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