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

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