Translations

Translations

Today, we learned more about Translations. 

Translations are horizontal and vertical movements (shifts) using basic shape. 

• The word Translation means to slide a graph. 

There are some rules when it comes to shifting. Stated below are the rules. 

VERTICAL TRANSLATIONS

* We call k a vertical translation. 

y=f(x) + k          - The entire graph shifts UP k units. 

Why? Because k is positive, which means we move up. 

y=f(x) - k          - The entire graph shifts DOWN k units

The position of the graph is influenced by k. The statement above says that k is a negative. Therefore, the graph will move down. The value of x does not change.

NOTE: h values are read as OPPOSITE, while k values are to remain the way they are. 

HORIZONTAL TRANSLATIONS

* We call h a horizontal translation. 

y=f(x-h)          - The entire graph shifts h units to the RIGHT.

y=f(x+h)         - The entire graph shifts h units to the LEFT.

The position of the graph is also influenced by h. The value of y does not change. 

For example:

If you are asked to sketch a graph of the function f(x - 9) - 3 on a Cartesian plane, 

with k= -3 and h=9, you will have to move 3 units down, since our k is a negative, and 9 units to the right, since we read h as its opposite (In this situation, -9 will be 9. It will become positive)