https://file.aiquickdraw.com/mathbot/file/17280570823769ftx29fs.jpg

The image shows a piecewise function \( h(x) \) with different expressions depending on the value of \( x \). The task is to find the values of \( h(-10) \), \( h(0) \), \( h(5) \), and \( h(6) \) based on the following piecewise definition of the function:

\[
h(x) = 
\begin{cases} 
-4x - 14 & \text{for } x < -8 \\
5 & \text{for } -8 \leq x < 5 \\
x + 4 & \text{for } x \geq 5
\end{cases}
\]

### Let's find the values one by one:

1. **\( h(-10) \):**
   Since \( -10 < -8 \), we use the first part of the function: \( h(x) = -4x - 14 \).
   \[
   h(-10) = -4(-10) - 14 = 40 - 14 = 26
   \]
   So, \( h(-10) = 26 \).

2. **\( h(0) \):**
   Since \( -8 \leq 0 < 5 \), we use the second part of the function: \( h(x) = 5 \).
   \[
   h(0) = 5
   \]

3. **\( h(5) \):**
   Since \( 5 \geq 5 \), we use the third part of the function: \( h(x) = x + 4 \).
   \[
   h(5) = 5 + 4 = 9
   \]

4. **\( h(6) \):**
   Since \( 6 \geq 5 \), we use the third part of the function: \( h(x) = x + 4 \).
   \[
   h(6) = 6 + 4 = 10
   \]

### Final answers:
- \( h(-10) = 26 \)
- \( h(0) = 5 \)
- \( h(5) = 9 \)
- \( h(6) = 10 \)

Would you like more details or have any questions?

Here are some follow-up questions for practice:
1. What is \( h(-9) \)?
2. Can you describe the behavior of \( h(x) \) as \( x \to -\infty \)?
3. What happens to \( h(x) \) as \( x \to +\infty \)?
4. How would the graph of \( h(x) \) look like?
5. For what values of \( x \) is \( h(x) \) a constant function?

**Tip:** Piecewise functions change their behavior depending on different intervals. Always check the interval before substituting values.

For the piecewise function, find the values h(-10), h(0), h(5), and h(6). The piecewise function is defined as: h(x) = -4x - 14 for x < -8; h(x) = 5 for -8 <= x < 5; h(x) = x + 4 for x >= 5.

This problem involves evaluating a piecewise function at specific values. The function is defined with different expressions depending on the value of x. Learn how to calculate h(-10), h(0), h(5), and h(6) with a detailed solution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation