What does f(x)=-f(-x) mean if f(2)=0?

Question

My assignment is to sketch a graph of y=f(x) with the Domain: (-infinity, -1)and (1,infinity). I can't figure out how to use the equation given. Please help!

Answer 1

The condition f(-x)=-f(x) means that f(x) is odd. Graph of odd function is symmetric w.r.t z axis, For example f(x)=x³ Now you have f(2)=0, which means that f(x) has zero at point x=2 and its graph crosses x-axis at x=2. To get an idea how the graph should look like, first you can draw graph of the function, for instance, f(x)=x³-4x or f(x)=-x³+4x (or any other  function which satisfies both conditions).