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Is a linear function even or odd or neither?

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You use an even function if f(-x) = f(x) for all x.You use an odd function if f(-x) = -f(x) for all x.and you use neither if there is at least one point for which one or the other of the above is not true.Most functions are neither even nor odd.

Looking at the graph of the function can give you a good idea. However, to actually prove that it is even or odd may be more complicated. Using the definition of "even" and "odd", for an even function, you have to prove that f(x) = f(-x) for all values of "x"; and for an odd function, you have to prove that f(x) = -f(-x) for all values of "x".

It is neither odd nor even. Only whole numbers can be odd or even.

8.5 is neither odd nor even. Only integers (whole numbers) are called odd or even. All other numbers (like fractions) are neither odd nor even.

Neither. Only integers are odd or even.

Neither. The property of odd or even is relevant only for integers.

Neither because only whole numbers can be odd or even

Only integers are called odd or even. 7.32 is not an integer, therefore it is neither odd nor even.

Only integers are called "odd" or "even." 6.87 is not an integer, hence it is neither odd nor even.

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

*1 is an odd number * 0 is an even number

Neither. Odd and even refer to integers.

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

No, zero is an even integer.

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.

The concept of odd and even can only be applied to integers. So 3.5 is neither odd nor even.

Neither. The property of odd or even applies only to integers (whole numbers).

No. Zero is neither an odd or an even number.

An even function is symmetric around the vertical axis. An odd function - such as the sine function - has a sort of symmetry too - around the point of origin. If you graph this specific function (for example, on the Wolfram Alpha website), you can see that the function has none of these symmetries. To prove that the function is NOT even, nor odd, just find a number for which f(x) is neither f(-x) nor -f(-x). Actually proving that a function IS even or odd (assuming it actually is) is more complicated, of course - you have to prove that it has the "even" or the "odd" property for EVERY value of x. Let f(x) = 2x3 - x2. Notice that f is defined for any x, since it is a polynomial function. If f(-x) = f(x), then f is even. If f(-x) = -f(x), then f is odd. f(-x) = 2(-x)3 - (-x)2 = -2x3 - x2 Since f(-x) ≠ f(x) = 2x3 - x2, f is not even. Since f(-x) ≠ - f(x) = -(2x3 - x2) = -2x3 + x2, f is not odd. Therefore f is neither even nor odd.

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

Decimal numbers generally are not considered to be odd or even. Only integers are odd or even. So on that basis, 3.6 is not an odd number, but neither is it an even number.

Yes, irrational numbers are neither odd nor even.

Neither, only whole numbers (not fractions or decimals) can be classified as odd or even numbers.

The property of parity (odd or even) applies to integers, not fractions. So 160.121 is neither odd nor even.


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