Transformations 1

This can occur with any function or point on a graph.

This can also occur with any function or point on a graph.

We know this would affect the $y$ coordinate, as $f(x)-a$ moves the graph down.

Therefore, the new point would move from $(2,5)$ to $(2,3)$, as the y coordinate would now be 2 units less than previously.

This is slightly counter-intuitive, as you may expect positive to move right. However, this translation moves any function or point to the left.

A negative value of $a$ means that we move any function or point to the right

This time, we know it affects the $x$ coordinate, as $f(x-3)$ moves the graph horizontally. Remember, this moves the graph to the right.

By moving right, the x-coordinate increases in size by 3 units. Therefore, the coordinate moves from $(2, 5)$ to $(5,5)$