Evaluating discrete functions

what we have here is a visual depiction of a function and this is a depiction of y is equal to H of X now what a lot of people see function notation like this they can they see it as somewhat intimidating until you realize what it's saying all a function is is something that takes an input in this case it's taking X as an input and then the function does something to it and then it spits out some other value which is going to be equal to Y so for example what is H of 4 based on this graph that you see right over here pause this video and think through that well all H of 4 means is when I input 4 into my function H what why am i spitting out or another way to think about it when X is equal to 4 what is y equal to well when X is equal to 4 my function spits out that Y is equal to 3 we know that from this point right over here so Y is equal to 3 so H of 4 is equal to 3 let's do another example what is H of 0 pause the video try to work that through well all this is saying is is if I input x equals 0 into the function what is going to be the corresponding Y well X when x equals 0 we see that Y is equal to 4 so it's as simple as that given the input what is going to be the output and that's what these points represent each of these points represent a different output for a given input now it's always good to keep in mind one of the things that makes it a function is that for given X at you input you only get one Y for example if we had two dots here then all of a sudden we or we have two dots for x equals 6 now all of a sudden we have a problem at figuring out what H of 6 would be equal to because it could be equal to 1 or it could be equal to 3 so if we had this extra dot here and this would no longer be a function in order for it to be a function for any given X it has to output a unique value it can't output two possible values now the other way is possible it is possible to have two different X's that output the same value for example if this was circled in what would H of negative 4 be well H of negative 4 when X is equal to negative 4 when you put that into our function it looks like the function would output 2 so H of negative 4 would be equal to 2 but H of 2 is also equal to we see very clearly there when we input a 2 into the function the corresponding Y value is 2 as well so it's ok for two different X values to map to the same y value that works but if you had some type of an arrangement some type of a relationship where for given x value you had 2 different Y values then that would no longer be a function but the example they gave us is a function assuming I don't modify it