I'm struggeling a bit with the transformations of a function when values are changed (for instance an offset to the right etc).
So far I have found the following: http://www.drcruzan.com/Images/TransformationEquation.png
Are there more transformations that I should look into? Any recommended sites, where aI can see them graphically?
The simplest transformations of the graph $y=f(x)$ are these:
$y=f(x+a)$ moves $a$ units in the negative $x$ direction
$y=f(x)+a$ moves $a$ units in the positive $y$ direction
$y=f(ax)$ scales by a factor $1/a$ about the $y$-axis
$y=af(x)$ scales by a factor $a$ about the $x$-axis
$y=f(-x)$ reflects about the $y$-axis
$y=-f(x)$ reflects about the $x$-axis
$y=f^{-1}(x)$ reflects about the line $y=x$ (if the inverse exists)
$y=\left|f(x)\right|$ reflects the negative parts of $f(x)$ about the $x$ axis
$y=f(\left|x\right|)$ reflects the half of the graph with negative $x$ about the $y$ axis