About this video
The video shows a function H as a set of dots on a graph, where y = H(x). It explains that H(4) means the output when the input is 4, reads H(4) = 3 and H(0) = 4 from the graph, and explains that a function gives only one output for each input, although two inputs can share the same output.
You'll be able to
- evaluate a function like H(4) by reading a graph of points.
- explain that a function gives exactly one output for each input.
- recognise that two different inputs may give the same output.
Key words
- function
- A rule that takes an input and gives exactly one output.
- input
- The value you put into the function, usually x, read on the horizontal axis.
- output
- The value the function gives back, usually y, read on the vertical axis.
- function notation
- Writing H(x) to mean the output of function H when the input is x.
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.
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