A2 5.5 Some Functions Have Symmetry

The table show Clare's elevation on a Ferris Wheel at different times, t. Clare got on the ride 80 seconds ago. Right now, at time 0 seconds she is at the top of the ride.

Assuming the Ferris Wheel moves at a constant speed for the next 80 seconds, complete the table.

​5.1: Changing Heights

Functions are "EVEN" if they are symmetric about the y-axis.

This means the function is "split in half" by the y-axis.

​EVEN Functions

Functions are "ODD" if they are symmetric about ORIGIN.

This means the function is reflected diagonally between quadrants.

​ODD
Functions

If a function is EVEN, the points on the graph will have:

SAME y-values for
OPPOSITE x-values.

For example, the point (-6, -5) becomes (6, -5).

This must be true for ALL points!

​Tables of EVEN Functions

If a function is ODD, the points on the graph will have:

OPPOSITE x-values and y-values for corresponding points.

For example, the point (-4, 5.25) become the point (4, -5.25)

This must be true for ALL points!

​Tables of ODD Functions