Q:

Function g is defined below.g(x) = f(x +2) - 5Complete the statements about the effects of the transformations on the graph of function f to obtain the graph of function g.The graph of function f is shifted right, down, left, or up 2 units and up, right, left, or down 5 units.If the point (4,-3) is on the graph of function f, then the point ( 2,6, 9, or -1 , -1, -8, 2, or -5 ) is on the graph of function g.

Accepted Solution

A:
Rule: if you have graph of function y=f(x) and a>0, then:
1. y=f(x-a) is translation a units right;
2. y=f(x+a) is translation a units left;
3. y=f(x)-a is translation a units down;
4. y=f(x)+a is translation a units up;

Since g(x)=f(x+2)-5, then firstly you have to translate the graph of function y=f(x) two units left and secondly 5 units down.