Vertical translation

Functions and graphs: Transformations of graphs and functions

Vertical translation

For any function $f$ and any number $d$ , the graph of the function $g$ defined by $g(x)=f(x)+d$ is obtained from the graph of $f$ by shifting it $d$ upwards (if $d<0$ , then it is basically a downward vertical shift of the graph).

If $\bigl(x,f(x)\bigr)$ a point on the graph of $f$ , then $\bigl(x,g(x)\bigr)=\bigl(x,f(x)+d\bigr)$ is a point on the graph of $g$ : for the same horizontal coordinate, $d$ has been added to the vertical coordinate.

The figure below shows the graphs of the functions $f(x)=x(x+1)(x-2)$ and $g(x)=x(x+1)(x-2)-2$ . So: $g(x)=f(x)-2$ .

You get the graph of $g$ by moving that of $f$ down by two.

verticale verschuiving