odd function
A function y=f(x) is odd when f(-x)f(x) for each x in the domain of f
An odd function is a mathematical function that satisfies the property that for any value of x, f(-x) = -f(x). In other words, an odd function is symmetric about the origin.
For example, the function f(x) = -x^3 is an odd function. To see this, we can substitute -x into the function and simplify as follows:
f(-x) = -(-x)^3 = -(x^3) = -f(x)
Similarly, the function g(x) = sin(x) is also an odd function. To see why, we can use the fact that sin(-x) = -sin(x) for any value of x.
Odd functions are characterized by having rotational symmetry of 180 degrees about the origin. This means that if we were to graph an odd function, and then rotate the graph 180 degrees about the origin, we would obtain the same curve.
It is important to note that not all functions are odd, and some functions may satisfy a different kind of symmetry, such as even functions or periodic functions.
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