Question

15 fill in the blank 1 point a function is shown below. $h(x)=\

$$\begin{cases}\\frac{-1}{2}x - 15, \\text{for } x \\leq -4 \\\\ 20 - 3x^2, \\text{for } x > -4\\end{cases}$$

$ what is the value of $h(-4) + 3h(-2)$? -97

Explanation:

Step1: Calculate $h(-4)$

Since $-4 \leq -4$, use $h(x)=\frac{-1}{2}x - 15$.

$$\begin{align*} h(-4)&=\frac{-1}{2}(-4) - 15\\ &=2 - 15\\ &=-13 \end{align*}$$

Step2: Calculate $h(-2)$

Since $-2 > -4$, use $h(x)=20 - 3x^2$.

$$\begin{align*} h(-2)&=20 - 3(-2)^2\\ &=20 - 3(4)\\ &=20 - 12\\ &=8 \end{align*}$$

Step3: Compute $h(-4)+3h(-2)$

Substitute the values found above.

$$\begin{align*} h(-4)+3h(-2)&=-13 + 3(8)\\ &=-13 + 24\\ &=11 \end{align*}$$

Answer:

11