Question

Describe the transformation that takes f (x)=x+1 to g (x)= - x+4.

Answer 1

f(x) = x+1
-1*f(x) = -1*(x+1) .... see note 1
-f(x) = -x-1
-f(x)+5 = -x-1+5 ... see note 2
-f(x)+5 = -x+4

note 1: multiplying both sides by -1 reflects the graph of f(x) over the x axis
note 2: adding 5 to -f(x) will shift the graph of -f(x) up by 5 units

So in short, the transformations that happen to go from f(x) to g(x) are
step 1) reflect over the x axis
step 2) shift up 5 units