Question

Function g is defined below.

g(x) = f(x +2) - 5

Complete 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.

Answer 1

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.

Answer 2

For the first question:
Always remember some general rules of transformation, which are
y= f(x+h)+ k
-Shifts the graph of f left h units if h> 0
-Shifts the graph of f right |h| units if h< 0
-Shifts the graph of f up k units if K> 0
-Shifts the graph of f down |k| units if k< 0

In our question ,
g(x) = f(x +2) – 5--------1
Graph of f is shifted left by two units due +2 in the given formula 1 and due to -5 graph of f is shifted down by 5 units.

For the second question:
By general notation of function,
y=f(x)
when x=4 then
-3=f(4)
In the formula 1, x must be 2 to get f(4) and after that by putting -3 in place of f(4) we get  
g(2)=f(2+2)-5
g(2)=-3-5
g(2)=-8
If the point (4,-3) is on the graph of function f, then the point (2,-8) will be on the graph of function g.