Name: Saima

Who is asking: Student
Level: Secondary

Is there a function that is both even and odd at the same time? In other words, is there a function that can pass the y-axis, x-axis, and origin symmetry test?

Hi Saima,

There are many graphs that pass all three symmetry tests, any circle with centre at the origin for example. If the curve is the graph of a function however the choices are much more limited. If (x,y) is on the graph of such a function then (x,-y) is also on the graph since it is symmetric in the x-axis. Since the graph is the graph of a function, y = -y. That is y = 0.

Hence Claude's answer to your question is "Yes there is one, but it is a really shy function that spends all of its time hiding behind the x-axis."

Claude and Penny
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