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Q: Can a function be both even and odd?

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

yes

f(x) = 0

Even (unless c = 0 in which case it is either or both!)

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

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

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.

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

The only way a function can be both even and odd is for it to ignore the input, i.e. for it to be a constant function. e.g. f(x)=4 is both even and odd. An even function is one where f(x)=f(-x), and an odd one is where -f(x)=f(-x). This doesn't make sense. Let's analyze. For a function to be even, f(-x)=f(x). For a function to be odd, f(-x)=-f(x). In this case, f(x)=4, and f(-x)=4. As such, for the first part of the even-odd definition, we have 4=4, which is true, making the function even. However, for the second part of it, we have 4=-4 (f(-x)=4, but -f(x)=-4), which is not true. Therefore constant functions are even because f(-x)=f(x), but not odd because f(-x)!=-f(x).

An even function is symmetric about the y-axis. If a function is symmetric about the origin, it is odd.

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

48 has both even and odd factors.

If the sum of two numbers is even, the two numbers are either both even or both odd. A few examples:2 + 4 = 6 (even + even = even)2 + 3 = 5 (even + odd = odd)5 + 2 = 7 (odd + even = odd)7+13 = 20 (odd + odd = even)

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

To determine whether a given number is odd or even: function odd_even($i) { return ($i % 2 == 0 ? 'even' : 'odd'); }

You have to look at the ones place digit for the quick way to this. If both ones digits are even then it will be even, if they are both odd then it will be even, if one is odd and one is even then it will be odd.

The 74180 is an 8 bit parity generator/checker.InputInputEven ControlOdd ControlEven OutputOdd OutputGroundInputInputInputInputInputInput+5VIf Even and Odd Control are both high, both Even and Odd Output are low.If Even and Odd Control are both low, both Even and Odd Output are high.If Even Control is low, and Odd Control is high, then Even Output is high if the number if inputs that are high is even, and Odd Output is the inverse of that. The reverse is true if Even Control is high and Odd Control is low.

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

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

45 percent are both even and odd digits

I have no idea about the signam function.The signum function is odd because sgn(-x) = -sgn(x).

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".

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