## A function has a single output.

This time, let’s have a look at how to determine a function by looking at how many outputs we can get by calculating the equations.

This time, let’s take a further step into the world of functions. Here, we’re going to test if the equation is a function or not by determining both domains and output results, aka range.

So, in function, the answer should be single. If the domain, argument of a function, is a, the output result (range) must be a single answer, b.

Take a look at image 01, where a’s output result is b, c’s output result is d, and e’s output result is f. In this case, this indeed is a function.

And here’s a graphical example: in this case, every single x’s output is a single y. And this is also a function.

And this is also another example that represents a function where every single x has a y value.

On the other hand, this is *NOT *a function. Every single x value has dual y outputs, meaning this is *NOT *a function.

Here, let’s compare the two. The left side represents a function since every single unique number has its unique counterparts. On the other hand, the right side doesn’t represent a function since 2 has two different outputs – 3 and 1.

Here’s a little tricky one – but this also represents a function. As long as the domains don’t have shared outputs, it represents a function.

Here are the other way around. Since 3 has dual outputs, it doesn’t represent a function.