Transcription
In the following table, is y a function of x?
In order for y to be a function of x, for any x that we input into our little function box--so let's say this is y as a function of x, it needs to spit out only one value of y. If it spit out multiple values of y, then it might be a relationship, but it's not going to be a function. So this is a function. This is a function.
If we had a situation where if we input x into a box, it could be multiple possible y's, then this is not a function.
So let's think about this table right over here. When x is equal to 1, we get y is equal to 1. But when x is equal to 1 again, all of a sudden, y is equal to 2. So here we have a situation where we input 1 into our little relationship box, and when we input 1 into our relationship box, we could get a 1, or we could get a 2 for y. So this is definitely not a function. For any input into a function, it has to map to exactly one output. Here it's mapping to two outputs. So this is not a function.