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Odd
- Each term, which in this case we only have one, is changed from positive to negative. So that means that this function is odd.
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f (-x) = (-x) 3 = - (x 3) for all values of x, as the cube of a negative number is the same as the negative of the cube of the positive value of the number. This implies f (-x) = -f (x), for all x. Hence, f (x) = x 3 is an odd function. Similarly, functions like x 5, x 7, x 9 etc. are odd functions.
I know because f(-2) equals a positive number - six - that the function isn't odd, but what about the symmetry? Odd functions don't have symmetry over the y-axis, right? So f(x) should be odd.
- 4 min
- Sal Khan
- sal said a car crashed. I thought he fell off his chair.
- A curve that is symmetric over the x-axis isn't a function, since it fails the vertical line test.
- Yes, that is the right mindset towards to understanding if the function is odd or even. For it to be odd: j(a) = -(j(a)) Rather less abstractly, *t...
- Yes because they must have symmetry around the origina. Tha's part of the definition of an odd function.
- The function is odd if `f(x) = -f(-x)`. The rule of a thumb might be that if a function doesn't intercepts y at the origin, then it can't be odd, a...
The derivative of an even function is odd. The derivative of an odd function is even. The integral of an odd function from −A to +A is zero (where A is finite, and the function has no vertical asymptotes between −A and A).
For example, if a function is a polynomial with both odd and even exponents, like "f(x) = x^2 + x^1", then the function is neither odd nor even. And there are many more examples as well. "f(x) = √x" is another example, as is "f(x) = log(x)", and "f(x) = 3^x", and countless others.
- 4 min
- Sal Khan
- If you use a graphing calculator, it is _neither_
- Yes, even functions are symmetric about the y axis, or f(-x) = f(x), and odd functions are symmetric about the origin, or -f(-x) = f(x).
- Zero is even and not odd, but f(x) = 0 is both an even and odd function!
- When you add the 4 to the sine, it shifts the whole function up four units, which means that it no longer meets the definition of an odd function....
- This function is an even function. And in the spirit of this video that connects "even" and "odd" functions with the parity (whether a number is ev...
About. Transcript. When we are given the equation of a function f (x), we can check whether the function is even, odd, or neither by evaluating f (-x). If we get an expression that is equivalent to f (x), we have an even function; if we get an expression that is equivalent to -f (x), we have an odd function; and if neither happens, it is neither!
- 4 min
This is a rational function. The process for checking if it's even, odd, or neither is the same as always. I'll start by plugging –x in for x: g (– x) = 3/ [ (– x) 2 + 2] = 3/ [ ( x2) + 2] = 3/ ( x2 + 2) I can see, by comparison, that this is the same as what I'd started with. So: g(x) is even.
In other words, a function f is odd if for every number x in its domain the number –x is also in the domain and f(-x) = -f(x). Note a function symmetric with the x-axis is not odd. In fact, a function symmetric with the x-axis is not a function of x at all, because it does not pass the vertical line test.
