No function ever really has to contain the origin if you constrain the domain to not include zero. Another way would be to just start graphing at x=1 and continue increasing x. In fact, you don't even have to graph at all since an odd function is defined as f(x) + f(-x) = 0
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An even function is symmetric about the y-axis. If a function is symmetric about the origin, it is odd.
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
if it is symmetric and centered at the origin, It is can be called an odd function
An even function is symmetric about the y-axis. An odd function is anti-symmetric.