Randall S. answered 03/20/21
Experienced HS/college math tutor
A is the vertical stretch. A>1 elongates the graph, A<1 compresses the graph. A<0 reflects the graph across the x-axis.
B is the horizontal shift. if you start at x=0 and then move horizontally, the quantity (x + B) is equal to zero when you substitute in for x the number you moved to. example - shift 5 to the right makes x equal to 5. what does B have to be for (5 + B) to be zero? B must be -5, so you would write that part of the function as (x - 5).
C is the vertical translation. C>0 means the graph moves up, C<0 means the graph moves down.
stretching f by a factor of 7, then shifting the graph of f to the right 2 units and upward 8 units ends up looking like
g(x) = 7f(x - 2) + 8