Question

1. find the value of $h$ at each given input.

a. $h(-6) =$
b. $h(0) =$
c. $h(2) =$
d. $h(7) =$
e. $h(0)+2h(10) =$

Explanation:

Step1: Locate x=-6 on the graph

Find the y-value at $x=-6$. The line has slope $m=2$ (from $x=-5,y=0$ to $x=0,y=10$? No, correction: from $x=-5,y=0$ to $x=-2,y=6$, slope $\frac{6-0}{-2-(-5)}=2$. Equation for left segment: $y=2(x+5)$. For $x=-6$: $y=2(-6+5)=2(-1)=-2$.

Step2: Locate x=0 on the graph

Find the y-value at $x=0$. The horizontal segment is at $y=6$.

Step3: Locate x=2 on the graph

Find the y-value at $x=2$. It is on the horizontal segment, so $y=6$.

Step4: Locate x=7 on the graph

Find the y-value at $x=7$. The right segment starts at $x=6,y=6$, slope $2$. Equation: $y=2(x-6)+6$. For $x=7$: $y=2(1)+6=8$.

Step5: Calculate $h(0)+2h(10)$

First, $h(10)$: use right segment equation $y=2(x-6)+6$. $h(10)=2(10-6)+6=8+6=14$. Then compute $6 + 2\times14=6+28=34$.

Answer:

a. $h(-6) = -2$
b. $h(0) = 6$
c. $h(2) = 6$
d. $h(7) = 8$
e. $h(0)+2h(10) = 34$