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The only function that can do this is f(x)=0, or y=0

What about y2-x2=0

Q: Can a function be even or odd at same time?

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No. In fact, no number can be both odd and even at the same time.

Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.

It can't happen.

Yes f(x)=0 is both even and odd

It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.

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No. In fact, no number can be both odd and even at the same time.

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

An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.

I find it convenient to express other trigonometric functions in terms of sine and cosine - that tends to simplify things. The secant function is even because it is the reciprocal of the cosine function, which is even. The tangent function is the sine divided by the cosine - an odd function divided by an even function. Therefore it is odd. The cosecant is the reciprocal of an odd function, so it is naturally also an odd function.

An even function is symmetric about the y-axis. An odd function is anti-symmetric.

both

Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.

It can't happen.

Yes f(x)=0 is both even and odd

An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2. A function can be either.

For an even function, f(-x) = f(x) for all x. For an odd function, f(-x) = -f(x) for all x.