Symmetric function

Hey there kiddo! Okay, so let’s talk about symmetric functions. Do you remember the word “symmetry” from when we talked about shapes and patterns? When something is symmetric, it has a balance and looks the same on both sides.

Well, when we talk about functions being symmetric, we mean that they have that same balance in their inputs and outputs. In math, a function takes in one or more variables and gives you an output.

Let's use an example: imagine you get an allowance for doing chores. If your allowance increases by five dollars every week, and you've been getting it for three weeks, we could write that out as a function like this:

Allowance = 5 x Week

So for week 1, you would get 5 x 1 = $5, for week 2, 5 x 2 = $10 and so on. Now, let's say we have another function:

Something = 5 x Week

This is also symmetric because the function is the same for every week as the previous function. So whether we plug in week 1, week 2, or any other week, the output is always the same.

Does that make sense? A symmetric function is one where the input and output have a balanced pattern and are the same for multiple inputs.