I was doing some functions review and learned about how to plot new coordinates for a transformed graph using the mapping rule.

(x,y) (x/b + c, ay + d)

This concept seems to work with most types of functions such as quadratic and sine functions. However, for exponential functions this does not seem to be working.

For 2^x some coordinates include (0,1), (2,4), (4,16)...

When I want to apply a transformation of y = 3^(x+2) - 1, I get a mapping rule of (x-2, y-1).

So now when I take the coordinates of the parent function and sub them into this rule I get (-2,0), (0,3), (2,15)...

Using demos and graphing this, these coordinates are not part of the graph? Does this rule not apply to this function?