Catalog of Some Elementary Functions

parent function

cubic (or odd power)

constant

linear

quadratic (or even power)

cubic (or odd power)

f(x)=a[w(x-h)

p

]\),

+k

a

1

h

0

k

0

w

1

2

3

reset

absolute value

square root or

th

n

root

function

graph

domain

range

This Demonstration presents a catalog of some elementary functions (no transcendental functions like sine or log included) that can be used to illustrate how each of the parent functions can be transformed by varying different parameters. The transformations include shift, reflection, stretch, and shrink in both horizontal and vertical directions. You can show or hide the domain, range, or graph of the function as well as the expression representing it.