what type of transformation is f(x)-4

Question

I want to describe in words , the transformations that would take place to f(x)

Answer 1

For f(x) - 4 the transformation is a drop of 4 in the output... The graph moves down 4 units

 

Example:  f(x) = 2x+7           f(x)-4 = 2x+3

              

                x    2x+7                 x       2x+3   

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

                -1     5                     -1       1

                 0     7                       0      3

                 1     9                       1      5

 

As can be seen the graph translates down 4 units

 

If we had f(x-4) then we would have a translation to the right.

 

Example:  f(x) = 2x+7       f(x-4) = 2(x-4)+7 = 2x-1

 

                 x       2x+7            x    2x-1

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

                -1        5                  3    5

                 0        7                  4    7

                 1        9                  5    9

 

As can be seen, to get the same output we have to move the x value 4 units to the right.

Thus, f(x-4) is a translation 4 units to the right.

 

If we added a value outside the function, such as f(x)+4, the graph would
translate upward 4 units.
If we added a value inside the function, such as f(x+4), the graph would
translate left 4 units.

Answer 2

Odalys,

 

Subtracting a value within a function shifts that function to the right that many units.

 

Subtracting a value outside of the function shifts the function that many units down.

 

Hope this helps! 

 

 

Jacoby