This week in Math 10 we did our Functions & Relations unit. In this unit we quickly covered a few different topics but in this blog post I will focus on functions. I will explain what a function is and how to identify one in any type of graph or table.
What is a function? A function is when none of the input numbers are the same unless they share the same output number. So what’s the difference between a function and a relation? A relation is the relationship between the input and output numbers and a function is just one output for each input. A relation is a vast term, while a function is more specific.
In this example with the coordinates, I can identify that the relationship between these numbers is a function. There is no one way to identify if it is a function. You just need to go through all the input numbers and make sure they all have their own unique output.
In this example using a table of values I can see this is a function because same thing with the coordinates, all in the input numbers have their own individual output numbers. I find a table of values makes it easier to identify because they go down in a row.
In this table of values I can see that one is an input twice. Because they share the same output this is a function. If the 5 were any other number except for 5 this would just be a relation.
If you are given a graph like this the first step is to write down all the coordinates and then identify if it is a function or not.
Now that I have written out all the coordinates I can see this graph represents a function.
Functions are very easy to identify once you understand what one is. Something that confused me when first learning about function was that if an input number is put in twice it is still a function as long as the output is the same. To easily identify is it as a function write it out in way that works best for you. If it is given to you in the form of coordinates write it out as a table of values if that would help you!
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