SOLUTION: If the point P given below is on the graph of a function f, find the corresponding point on the graph of g. P= (2,7), g(x)=f(x-3)-2

Algebra ->  Rational-functions -> SOLUTION: If the point P given below is on the graph of a function f, find the corresponding point on the graph of g. P= (2,7), g(x)=f(x-3)-2      Log On


   

Question 1151527: If the point P given below is on the graph of a function f, find the corresponding point on the graph of g.
P= (2,7), g(x)=f(x-3)-2
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given


    f(2) = 7.


It is the exact meaning of this fragment  from the post  "the point P = (2,7) is on the graph of a function f".


Take  x-3 = 2,  i.e.  x = 2+3 = 5.   

Then  

      g(5) = f(x-3) - 2 = f(5-3) - 2 = f(2) - 2 = (at this point recall that f(2) = 7, so you can continue the equality) = 7 - 2 = 5.


Thus the corresponding point on the graph of the function g  is  Q = (5,5).


ANSWER.  The corresponding point on the graph of the function g  is  Q = (5,5).

------------

The lesson to learn from my post is THIS : 

    The "corresponding point" in this context is the point, whose coordinates you can calculate, 
    starting from the given point P and using the given definition of the function g.