What is the scale factor for this dilation? How do you
know?

Look at the left-most part of the blue diagram. It is 1 unit high. The corresponding left-most part of the red diagram is 2 units high, which is twice as high as the blue portion it corresponds to.

The scale factor tells us how to enlarge or shrink the object. In this case, the red figure is twice as tall and wide compared to the blue figure.

You can pick any pair of corresponding sides to get the scale factor.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2