Even and Odd Functions Question?

Question

If g(x) has a domain of all real numbers, name one point on the graph and explain why it must be on the graph

NOTE: g(x) is an odd function

Answer 1

I'll give you a hint. By the way, there's an implied condition that the function g(x) is continuous. If the function is not continuous, this question won't have an answer.

An odd function has the property that g(-x)=-g(x)

Try any function that has this property. Start these few first:

g(x)=x
g(x)=x^3
g(x)=sin(x)
g(x)=x+x^3+sin(x)

See what point all these functions have in common. That's the point that must exist on a continuous odd function.