Why are odd functions symmetric about the origin?

f(x) is odd—it is symmetrical with respect to the origin—because f(−x) = −f(x). Answer. f(x) is even—it is symmetrical with respect to the y-axis—because f(−x) = f(x). Note: A polynomial will be an even function when all the exponents are .

Why is a function said to be symmetrical about the origin?

Mathwords: Symmetric with Respect to the Origin. Describes a graph that looks the same upside down or right side up. Formally, a graph is symmetric with respect to the origin if it is unchanged when reflected across both the x-axis and y-axis.

Is the domain of each odd function symmetric about the origin?

A function is said to be an odd function if its graph is symmetric with respect to the origin.

Is symmetric about the origin even or odd?

A function with a graph that is symmetric about the origin is called an odd function. Note: A function can be neither even nor odd if it does not exhibit either symmetry. For example, f(x)=2x f ( x ) = 2 x is neither even nor odd.

How do you tell if a function is symmetric about the origin?

Correct answer: For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x), and the resulting function must be equal to the original function. So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.

Does an odd function have to go through the origin?

The inverse function y = 1/x is odd, but it does not pass through the origin (its domain is nonzero real numbers). If an odd function has zero in its domain, then it must pass through the origin. The reason is that by definition of an odd function, f(-x) = -f(x) for all x in the domain.

Do odd functions have to pass through the origin?

Do all odd functions go through the origin?

Does an odd function always pass through the origin? – Quora. Yes, if it’s defined at . A function is said to be an odd function if for all in its domain, . So if is defined, then which implies , in which case, its graph includes the point .

Are odd functions and even functions symmetric?

The function is odd if f(-x) = -f(x). An even function has reflection symmetry about the y-axis. An odd function has rotational symmetry about the origin.