Horizontal translation

Functions and graphs: Transformations of graphs and functions

Horizontal translation

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