Even Function: Frequently Asked Questions
How to check a function is even or not?
For an even function, f(-x) = f(x) equality holds true for every real number x for which f(x) is defined.
Give some examples of even functions.
Examples of even functions are x2, cos(x), sec(x), |x|, etc.
Are all polynomial functions even?
No, polynomial functions which involve only even powers of the independent variable are even functions. Those involving odd powers wouldn’t follow the property f(-x) = f(x).
Can a function be even as well as odd?
Yes, the zero function is both even and odd because for all values of x, f(-x) = -f(x) = f(x) = 0.
Is Cos x an even function?
Yes, cos x is an even function as cos(-x) = cos x.
Even Function
Even function is defined as a function that follows the relation f(-x) equals f(x), where x is any real number. Even functions have the same range for positive and negative domain variables. Due to this, the graph of even functions is always symmetric about the Y-axis in cartesian coordinates.
In this article, we will learn about even functions, their examples, properties, graphical representation of even functions, some solved examples, and practice questions related to even functions.
Table of Content
- What is an Even Function?
- Graphical Representation of an Even Function
- Properties of an Even Function
- Even Function and Odd Function Difference