For the piecewise​ function, find the values ​h(negative 10​), ​h(negative 7​), ​h(1​), and ​h(4​).
h left parenthesis x right parenthesis equals StartSet Start 3 By 1 Matrix 1st Row 1st Column negative 3 x minus 10 comma for x less than minus 8 2nd Row 1st Column 1 comma for minus 8 less than or equals x less than 1 3rd Row 1st Column x plus 5 comma for x greater than or equals 1 EndMatrix 
 
Question content area bottom
Part 1
​h(negative 10​)equals
  
enter your response here
Part 2
​h(negative 7​)equals
  
enter your response here
Part 3
​h(1​)equals
  
enter your response here
Part 4
​h(4​)equals
  
enter your response here

The piecewise function is given as:

\[
h(x) = 
\begin{cases} 
-3x - 10 & \text{for } x < -8 \\
1 & \text{for } -8 \leq x < 1 \\
x + 5 & \text{for } x \geq 1 
\end{cases}
\]

Now, let's calculate the specific values for \(h(x)\):

### Part 1: \(h(-10)\)
Since \(-10 < -8\), we use the first part of the function: \(h(x) = -3x - 10\).
\[
h(-10) = -3(-10) - 10 = 30 - 10 = 20
\]
Thus, \(h(-10) = 20\).

### Part 2: \(h(-7)\)
Since \(-8 \leq -7 < 1\), we use the second part of the function: \(h(x) = 1\).
\[
h(-7) = 1
\]
Thus, \(h(-7) = 1\).

### Part 3: \(h(1)\)
Since \(1 \geq 1\), we use the third part of the function: \(h(x) = x + 5\).
\[
h(1) = 1 + 5 = 6
\]
Thus, \(h(1) = 6\).

### Part 4: \(h(4)\)
Since \(4 \geq 1\), we again use the third part of the function: \(h(x) = x + 5\).
\[
h(4) = 4 + 5 = 9
\]
Thus, \(h(4) = 9\).

### Final Answers:
1. \( h(-10) = 20 \)
2. \( h(-7) = 1 \)
3. \( h(1) = 6 \)
4. \( h(4) = 9 \)

Would you like further details on the piecewise function? Here are five related questions:

1. What is the domain of this piecewise function?
2. How would the graph of this piecewise function look?
3. Can we find the range of the function based on these equations?
4. What happens if \(x = -8\)? Which part of the function should we use?
5. How would the function behave as \(x \to \infty\)?

**Tip:** Always check which condition applies to the value of \(x\) before calculating a piecewise function.

For the piecewise​ function, find the values ​h(negative 10​), ​h(negative 7​), ​h(1​), and ​h(4​).
h(x) = {
-3x - 10, for x < -8
1, for -8 ≤ x < 1
x + 5, for x ≥ 1
}

Learn how to solve a piecewise function with three parts: h(x) = -3x - 10 for x < -8, h(x) = 1 for -8 ≤ x < 1, and h(x) = x + 5 for x ≥ 1. This step-by-step guide calculates h(-10), h(-7), h(1), and h(4), and is suitable for students in Grades 9-11.

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