Question

can someone answer #9

Answer 1

Solution:

First i'm going to divide the graph into 3 parts. Linear, Quadratic and Horizontal graph.

Linear:

$Slope=\frac{-2-0}{-4-(-2)}=1\\y=m(x-xo)+yo\\y=1x-(-2)+(-4)\\y=x-2 , x\leq-1$

Quadratic:

$f(x) = a(x-h)^{2} + k\\f(x)=(x-2)^{2}-7,-1\leq x\geq 6$

Horizontal:

$f(x)=7,x\geq 6$

Answer:

$f(x)=x-2 , x\leq-1\\f(x)=(x-2)^{2}-7,-1\leq x\geq 6\\f(x)=7,x\geq 6$

Hope this was helpful.