For the piecewise function, find the values \( h(-8), h(2), h(5) \), and \( h(6) \) \( h(x)=\left\{\begin{array}{ll}-3 x-18, & \text { for } x<-6 \\ 5, & \text { for }-6 \leq x<5 \\ x+1, & \text { for } x \geq 5\end{array}\right. \) \( h(-8)=\square \)

To evaluate the piecewise function \( h(x) \) at the given values, we'll determine which piece of the function applies to each input and then compute the corresponding output. The piecewise function is defined as: \[ h(x)= \begin{cases} -3x - 18, & \text{for } x < -6 \\ 5, & \text{for } -6 \leq x < 5 \\ x + 1, & \text{for } x \geq 5 \end{cases} \] Let's evaluate each requested value: 1. **\( h(-8) \)** - **Determine the interval:** \( -8 < -6 \) - **Function to use:** \( h(x) = -3x - 18 \) - **Calculate:** \[ h(-8) = -3(-8) - 18 = 24 - 18 = 6 \] - **Result:** \( h(-8) = 6 \) 2. **\( h(2) \)** - **Determine the interval:** \( -6 \leq 2 < 5 \) - **Function to use:** \( h(x) = 5 \) - **Calculate:** \[ h(2) = 5 \] - **Result:** \( h(2) = 5 \) 3. **\( h(5) \)** - **Determine the interval:** \( 5 \geq 5 \) (i.e., \( x \geq 5 \)) - **Function to use:** \( h(x) = x + 1 \) - **Calculate:** \[ h(5) = 5 + 1 = 6 \] - **Result:** \( h(5) = 6 \) 4. **\( h(6) \)** - **Determine the interval:** \( 6 \geq 5 \) (i.e., \( x \geq 5 \)) - **Function to use:** \( h(x) = x + 1 \) - **Calculate:** \[ h(6) = 6 + 1 = 7 \] - **Result:** \( h(6) = 7 \) ### Summary of Results: \[ \begin{align*} h(-8) &= 6 \\ h(2) &= 5 \\ h(5) &= 6 \\ h(6) &= 7 \\ \end{align*} \]