 Manipulative 1: Parabola 

A line of symmetry is a
line
about which a geometric object or objects are reflection symmetrical. Manipulative 1
shows the line of symmetry of a parabola. If the parabola is reflected about
this line of symmetry it remains unchanged. Click on the light blue point labeled
'ClickNDrag' and drag it. Notice that the line of symmetry is
equidistant
from both sides of the parabola.
A function
may have an
inverse.
A function and its inverse are symmetrical around the line y = x.
Manipulative 2 shows the function y = x^{2}/4 and its inverse
y = (4x)^{1/3}. Click on the light blue point labeled 'ClickNDrag'
and drag it along the line y = x. Note that the line is equidistant from
the function and its inverse.

 Manipulative 2: Inverse functions 
