https://file.aiquickdraw.com/mathbot/file/1725672236028jx7804l0.jpg

It looks like I encountered an issue accessing the image. Let me attempt another method to analyze the content of the file and assist with solving the problem. I'll describe the piecewise function and solve for the given values \( H(-8), H(1), H(20), H(7) \) from the image.

The piecewise function appears as:

\[
H(x) =
\begin{cases}
-2x - 19, & \text{for } x < -6 \\
2, & \text{for } -6 \leq x \leq 2 \\
x + 7, & \text{for } x > 2
\end{cases}
\]

Let's compute the values for \( H(-8), H(1), H(20), H(7) \):

- For \( H(-8) \), since \( -8 < -6 \), use the formula \( -2x - 19 \).
- For \( H(1) \), since \( -6 \leq 1 \leq 2 \), use the constant value 2.
- For \( H(20) \), since \( 20 > 2 \), use the formula \( x + 7 \).
- For \( H(7) \), since \( 7 > 2 \), use the formula \( x + 7 \).

I'll now calculate these values.The values of the function \( H(x) \) for the given inputs are:

- \( H(-8) = -3 \)
- \( H(1) = 2 \)
- \( H(20) = 27 \)
- \( H(7) = 14 \)

Do you want further details or explanations?

Here are 5 related questions to explore:
1. What is a piecewise function and how does it work?
2. How can we graph a piecewise function like \( H(x) \)?
3. What happens if we extend the intervals in the function \( H(x) \)?
4. Can we find where \( H(x) \) is continuous or discontinuous?
5. What would be the value of \( H(x) \) for other negative values of \( x \)?

**Tip:** Always check the conditions for each piece of the function when evaluating values.

For the piecewise function, find the values H(-8), H(1), H(20), and H(7):
H(x) =
- 2x - 19, for x < -6
2, for -6 <= x <= 2
x + 7, for x > 2

Learn how to evaluate the piecewise function H(x) for specific values: H(-8), H(1), H(20), and H(7). This problem covers key concepts in piecewise functions and algebra, suitable for students in Grades 9-12.

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