p(x)={(-3x-2  x<=2),(4x^(2)+2x-7   x>2):}find p(-6)

The piecewise function is defined as:

\[
p(x) =
\begin{cases}
-3x - 2 & \text{if } x \leq 2 \\
4x^2 + 2x - 7 & \text{if } x > 2
\end{cases}
\]

To find \( p(-6) \), we first determine which part of the piecewise function to use. Since \( -6 \leq 2 \), we will use the first part of the function, which is \( p(x) = -3x - 2 \).

Now substitute \( x = -6 \) into this equation:

\[
p(-6) = -3(-6) - 2 = 18 - 2 = 16
\]

So, \( p(-6) = 16 \).

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

Here are 5 related questions to expand on this:

1. How would you find \( p(0) \)?
2. What is \( p(3) \) using the piecewise function?
3. How do you determine which part of a piecewise function to use?
4. What is the domain of this piecewise function?
5. Can you find where the two parts of the function meet at \( x = 2 \)?

**Tip:** When working with piecewise functions, always check which condition your input satisfies before substituting into the appropriate expression.

Learn how to evaluate a piecewise function at p(-6) by determining which part of the function applies and substituting the value. This problem covers piecewise functions, linear equations, and quadratic functions, suitable for students in Grades 9-11.

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