*Terms:*

**Input** – X-axis

**Output**– Y-axis

This week in math, I learned about functions which are special relations. They are different from relations because relations have many multiple outputs on the input. For example, if we write out the multiples of 4,5, and 6 there are many multiples out of the three that have numbers in common. If we translate that information onto a chart, you notice that there are three possibilities on the x-axis which are 4,5, and 6. It is even easier to tell if the numbers are a relation once it’s been transitioned onto a graph. You would notice more than one dot on the same line which means it wouldn’t pass the vertical line test.

If we were to find the principle square root of 2,3, and 4 it would be 4,9, and 16. This is a function because for every input there is only one output. If we were to put this on a graph, the dots are plotted out on different points and it does pass the vertical line test.

Functions can also be described using scientific notation. For example, x= 3x+2. If “x” was 2 then the answer would be 8. Whatever gets put in, gets put out. This can be put into a coordinate which would be (2,8). However, if “x” was already given to you, you would solve an equation. If “x” was 35, then you would subtract 2 from each side and isolate the variable (divide). As a result, the answer would be 11.