Understanding Relations and Functions
Think of a relation as a matchmaker that connects values from one group (the domain) to another group (the range). It's basically a set of ordered pairs like (x,y) where x gets paired with y.
Now here's where it gets interesting - a function is a special type of relation with one important rule: each x-value can only be matched with one y-value. No cheating allowed! If you see an x-value trying to connect to multiple y-values, it's not a function.
For example, f = {(1,2), (2,3), (3,5)} is a function because each x has its own unique y. But g = {(1,3), (1,4), (2,5)} isn't a function because x = 1 is trying to pair with both 3 and 4.
Quick Tip: Functions use the notation f(x) = y, which reads as "f of x equals y." This just means when you input x, you get y as the output.