# How can you tell if the graph of a function is odd?

## How can you tell if the graph of a function is odd?

If a function is even, the graph is symmetrical about the y-axis. If the function is odd, the graph is symmetrical about the origin. Even function: The mathematical definition of an even function is f(–x) = f(x) for any value of x.

**Which function is an odd function?**

An odd function should hold the following equation: f(-x) = -f(x), for all values of x in D(f), where D(f) denotes the domain of the function f. In other words, we can say that the equation f(-x) + f(x) = 0 holds for an odd function, for all x.

**What is an example of an odd function?**

Odd Function Some examples of odd functions are y=x3, y = x 3 , y=x5, y = x 5 , y=x7, y = x 7 , etc. Each of these examples have exponents which are odd numbers, and they are odd functions.

### What makes a function even or 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 determine if a function is even or odd algebraically?**

In order to “determine algebraically” whether a function is even, odd, or neither, you take the function and plug −x in for x, simplify, and compare the results with what you’d started with.

**How do you determine whether the function is even odd or neither?**

How do you figure out, algebraically, if a function is even, odd, or neither? In order to “determine algebraically” whether a function is even, odd, or neither, you take the function and plug −x in for x, simplify, and compare the results with what you’d started with.

#### What is the graph of an odd function?

Graphical representation of odd function Odd Functions are symmetrical about the origin. The function on one side of x-axis x -axis is sign inverted with respect to the other side or graphically, symmetric about the origin. Here are a few examples of odd functions, observe the symmetry about the origin.

**How do you know if a function is odd?**

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) = x 3 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.

**What are the properties of odd and even functions?**

Properties of Odd functions 1 The sum of two odd functions is odd. 2 The difference of two odd functions is odd. 3 The product of two odd functions is even. 4 The quotient of two odd functions is even. 5 The composition of two odd functions is odd. 6 The composition of an even function and an odd function is even.

## How do you prove the definite integral of an odd function?

The integrand f (x) is an odd function and it is symmetrical about the origin. We see in most of the odd function graph that the region below and above the x-axis is symmetrical. We know that, area under the increasing curve is equal to the area under the decreasing curve. To prove the definite integral of an odd function zero: