Which Graph Represents An Odd Function

Which Graph Represents an Odd Function?

In mathematics, an odd function is a function whose output is equal to the negative of its output when the input is negated. In other words, if $f(x) = y$, then $f(-x) = -y$.

The graph of an odd function is symmetric about the origin. This means that if you reflect the graph across the origin, the reflected graph will coincide with the original graph.

Here are some examples of odd functions:

• $f(x) = x^3$
• $f(x) = \sin x$
• $f(x) = -\cos x$

Here are some examples of even functions:

• $f(x) = x^2$
• $f(x) = \cos x$
• $f(x) = \log x$

Questions

Here are some questions you can ask about which graph represents an odd function:

• Is the graph symmetric about the origin?
• Is the output of the function negative when the input is negative?

Example

Consider the following graphs:

[Graph 1] [Graph 2] [Graph 3] 

Which graph represents an odd function?

Answer

Graph 3 represents an odd function. The graph is symmetric about the origin, and the output of the function is negative when the input is negative.

Explanation

Graph 1 is not symmetric about the origin. Graph 2 is symmetric about the origin, but the output of the function is not negative when the input is negative. For example, the output of the function at $x = 1$ is 2, and the output of the function at $x = -1$ is also 2.

Graph 3 is symmetric about the origin, and the output of the function is negative when the input is negative. For example, the output of the function at $x = 1$ is -1, and the output of the function at $x = -1$ is also -1.