Horizontal translation

Functions and graphs: Transformations of graphs and functions

Horizontal translation

For any function $f$ and any number $c$ , the graph of the function $g$ defined by $g(x)=f(x+c)$ is obtained from the graph of $f$ by shifting this $c$ to the left (if $c<0$ , then it is basically a horizontal shift of the graph to the right ).

If $\bigl(x,f(x)\bigr)$ is a point on the graph of $f$ , then $\bigl(x-c,g(x-c)\bigr)=\bigl(x-c,f(x)\bigr)$ is a point on the graph of $g$ with the same vertical coordinate, but with a horizontal coordinate subtracted with $c$ . In other words, the point on the graph of $f$ has a corresponding point on the graph of $g$ by shifting it $c$ to the left (or to the right for negative $c$ ).

The figure below shows the graphs of the functions $f(x)=x(x+1)(x-2)$ and $g(x)=(x-2)(x-1)(x-4)$ . So: $g(x)=f(x-2)$ .

You get the red graph of $g$ by shifting the blue graph of $f$ two to the right.

horizontale verschuiving