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## Evaluating functions

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# Evaluating discrete functions

## Video transcript

- [Instructor] 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 when a lot of people see
function notation like this 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 four based on this graph that you see right over here? Pause this video and think through that. Well all H of four means
is when I input four into my function H what
Y am I spitting out? Or another way to think about
it, when X is equal to four, what is Y equal to? Well when X is equal to four,
my function spits out that Y is equal to three. We know that from this
point right over here, so Y is equal to three, so H
of four is equal to three. Let's do another example. What is H of zero? Pause the video try to work that through. Well all this is saying is
if I input an X equals zero into the function what is going
to be the corresponding Y? Well when X equals zero we
see that Y is equal to four. 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 that you input you only get one Y. For example if we had two dots
here, then all of a sudden or we have two dots for X
equals six, now all of a sudden we have a problem
figuring out what H of six would be equal to because
it could be equal to one or it could be equal to three. So if we had this extra dot
here, then 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 four be? Well H of negative four when
X is equal to negative four, you put that into our function
it looks like the function would output two. So H of negative four
would be equal to two. But H of two is also equal
to we see very clearly there, when we input a two into the
function, the corresponding Y value is two as well. So it's okay 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 a given X value you had two 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.