If f(x) = {3x+17x−4if −3<x<2if 3<x<6, then find the value of f(x) at x = -2.
-18
-5
-8
10

The function \( f(x) \) is defined piecewise with two different expressions depending on the interval of \( x \). The function appears to have an issue with formatting, so let's clarify it based on standard piecewise notation. It seems like the function should be written as:

\[
f(x) = 
\begin{cases}
3x + 17 & \text{if } -3 < x < 2 \\
x - 4 & \text{if } 3 < x < 6
\end{cases}
\]

To find the value of \( f(x) \) at \( x = -2 \), we need to determine which interval this value of \( x \) belongs to.

### Step 1: Identify the appropriate interval for \( x = -2 \)

Since \( -2 \) falls within the interval \(-3 < x < 2\), we use the first expression:

\[
f(x) = 3x + 17.
\]

### Step 2: Substitute \( x = -2 \) into the expression

\[
f(-2) = 3(-2) + 17.
\]

Calculating this gives:

\[
f(-2) = -6 + 17 = 11.
\]

It appears none of the provided answer choices match the correct calculation, suggesting there might be an error in the available options.

Would you like to double-check the intervals or clarify anything further? Here are some related questions to deepen understanding:

1. How do you handle piecewise functions when \( x \) is at the boundary of intervals?
2. What would be the value of \( f(x) \) at \( x = 0 \)?
3. How does the function behave between intervals?
4. What would be the value of \( f(x) \) if \( x = 4 \)?
5. Could boundary conditions alter the output of a piecewise function?

**Tip:** Always confirm the function’s interval before substituting values, especially with piecewise-defined functions.

If f(x) = {3x + 17 if -3 < x < 2; x - 4 if 3 < x < 6}, then find the value of f(x) at x = -2.

Learn how to evaluate piecewise functions by finding the value of f(x) at x = -2. This problem involves key concepts in piecewise and linear functions and is suitable for students in Grades 9-11.

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