What does it mean for a function to be even odd or neither?

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!

How do you know if a function is odd or even or neither?

Answer: For an even function, f(-x) = f(x), for all x, for an odd function f(-x) = -f(x), for all x. If f(x) ≠ f(−x) and −f(x) ≠ f(−x) for some values of x, then f is neither even nor odd.

What does it mean when a function is neither even or odd?

Video quote: When is a function neither even nor odd. It's going to be neither if you plug in negative x. And if you do not get negative f of X. So what does that mean. Well let's say if you replace X with

What is an even function?

Definition of even function



: a function such that f(x)=f(−x) where the value remains unchanged if the sign of the independent variable is reversed.

What is an example of an even function?

Even functions are those functions in calculus which are the same for +ve x-axis and -ve x-axis, or graphically, symmetric about the y-axis. It is represented as f(x) = f(-x) for all x. Few examples of even functions are x⁴, cos x, y = x², etc.

What is a odd function?

Definition of odd function



: a function such that f (−x) =−f (x) where the sign is reversed but the absolute value remains the same if the sign of the independent variable is reversed.

What is an odd function equation?

A function is odd if −f(x) = f(−x), for all x. The graph of an odd function will be symmetrical about the origin. For example, f(x) = x³ is odd. That is, the function on one side of x-axis is sign inverted with respect to the other side or graphically, symmetric about the origin.