Questions: For the piecewise function, find the values h(-9), h(-4), h(2), and h(3). h(x) = -2x - 13, for x < -8 2, for -8 ≤ x < 2 x + 7, for x ≥ 2

Transcript text: For the piecewise function, find the values $h(-9), h(-4), h(2)$, and $h(3)$. \[ h(x)=\left\{\begin{array}{ll} -2 x-13, & \text { for } x<-8 \\ 2, & \text { for }-8 \leq x<2 \\ x+7, & \text { for } x \geq 2 \end{array}\right. \]

Solution

Solution Steps

To find the values of the piecewise function at specific points, we need to determine which condition each point satisfies and then apply the corresponding expression. For each given value of $ x $, check the conditions in the piecewise function and compute the result using the appropriate formula.

Step 1: Evaluate $ h(-9) $

To find $ h(-9) $, we check which condition in the piecewise function it satisfies. Since $-9 < -8$, we use the expression $-2x - 13$.

\[ h(-9) = -2(-9) - 13 = 18 - 13 = 5 \]

Step 2: Evaluate $ h(-4) $

For $ h(-4) $, we determine the appropriate condition. Since $-8 \leq -4 < 2$, we use the constant value 2.

\[ h(-4) = 2 \]

Step 3: Evaluate $ h(2) $

To find $ h(2) $, we check the conditions. Since $2 \geq 2$, we use the expression $x + 7$.

\[ h(2) = 2 + 7 = 9 \]

Step 4: Evaluate $ h(3) $

For $ h(3) $, we determine the condition it satisfies. Since $3 \geq 2$, we use the expression $x + 7$.

\[ h(3) = 3 + 7 = 10 \]