Who is asking: Student
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."Cheers,
Claude and Penny