modulus function

graph plotting software

Graphmatica is a 'freeware' graph drawing package that seems good (and reliable).

asymptotes

asymptotes are where a function behaves curiously
it is important to know where these curious points are located when differentiating and integrating - to avoid difficulties

types of functions

functions: combined and inverse

 

this shows the reflection of a function with the inverse

two special functions are their own inverses:

the inverse trigonometric functions need a carefully chosen domain so that the function is one-to-one:

functions: graphical transforms

• putting a negative sign in front of the function ( -f(x)) reflects it in the x-axis
• replacing x by -x reflects the function (f(-x)) in the y-axis

this website shows the various transformations of a quadratic curve
using sliders

functions