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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?

Gerry Myerson
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Gildraths
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  • what is the effect when I have a function f(x) = x^2 and then change it to: f(x+3) whats the value then? – Gildraths Jun 21 '15 at 12:22
  • A good idea is to look at Geogebra and have a play with the slide bars. – Karl Jun 21 '15 at 12:24
  • @Karl Yes I played around with https://www.desmos.com/ , however I'm not sure if I have covered all the possibilites. For instance I haven't found what addin a number in the function (like my first comment) actually does – Gildraths Jun 21 '15 at 12:28

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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

danimal
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