Question

I am in pre-calculus and taking a placement exam and have no clue what I'm supposed to do for this problem. It's really important that I score well so could someone please explain how to do this? Also I'm not cheating because this isn't the question from my book or anything it is just one I made that is similar to the others.

The function f(x) passes through point (3, 5). If g(x) = f(x+2)-6, find a point that must fall on the graph of g(x).

Answer 1

remember, to move the graph of a function up, c units, add c to whole function
to move the graph of the function to the right, r units, minus r from every x

we see
f(x-(-2))+(-6)
moved up -6 units and to the right -2 units aka
moved down 6 units and to the left 2 units

minus 6 from y and minus 2 from x
(x,y)
(3,5)
3-2=1
5-6=-1
(1,-1) must be on the graph