Odd Functions: Properties And Examples

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.

More Answers:
Discovering The Vertex Of A Parabola: Formulas And Techniques
Mastering Quadratic Functions: Converting Standard Form To Vertex Form
Mastering The Basics: Parabolas – Definition, Equations, And Applications

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »