## Tutorial: New functions from old: Scaled and shifted functions

### Resources

Some basic functions

Here are the graphs of some common functions. Try to be able to instantly recognize each of them by its shape.
$f(x) = x$

$f(x) = x^2$

$f(x) = x^3$

$f(x) = \dfrac{1}{x}$

$f(x) = \sqrt{x}$

$f(x) = |x|$

**transformed**the function. Well, here are some "shift" rules that tell you the effect of transformations like this.

Shift rules

Shift rules tell us which transformations of a function result in the graph being shifted left, right, up, or down:
Scaling rules

In addition to shifting the graph of a function, we can also stretch or compress it vertically and/or horizontally. The scaling rules tell us which transformations of a function are needed to do this:
Of course, we can combine combine shifts and scales in sequence:
Flipping rules

Finally, in addition to shifting and scaling the graph of a function, we can also flip it vertically and/or horizontally. The following rules tell us which transformations of a function are needed to do this:
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Copyright © 2023 Stefan Waner and Steven R. Costenoble

*March 2023*Copyright © 2023 Stefan Waner and Steven R. Costenoble