Name: Saima

Who is asking: Student
Level: Secondary

Question:
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?

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."