Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

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Relations and Determining Whether a Relation is a Function - Problem 3

Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

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Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

One of the neat things about functions is that we know something is a function if each x has exactly one y but sometimes you are not given the points, you are not given numbers, all you are given is a funny graph. So what I want to talk about here is how you can tell that something is a function just based on the graph and you'll see it's actually pretty easy. It's using what's called the vertical line test.

So what I'm going to do is go through these graphs and draw vertical lines and if it hits, if my vertical line hits the graph more than once in each line then it's not a function, because that represents a place where an x value has two y values.

Let's check it out. Think of this like your pencil this is a big pencil. What you would do with the graph on your paper is take your pencil lay it down there and then move it across the graph, see if you hit any places on this graph where your pencil crosses the squiggly in more than one place. And you'll see in this graph there's like tons of places, check it out.

I just hit my graph like one two three four like 10 times whatever it doesn't matter, I hit it more than once so this is not a function. This x value right here whatever it is has tons the y values there is a y value, there is another one, there is no one it's not a function. Each x only gets one y value.

Let's try this next graph use your pencil and make sure it's vertical and not horizontal. Vertical oh-oh! You can see your pencil hits places where your vertical line crosses the graph in more than one place. That again means that x has two y values, not a function.

Here is a couple that are a little bit different when you use your vertical line test down here. Check it out everywhere I move my pen it only crosses the graph once right, I'm never hitting this graph line more than once. So this case yes it's a function because that x value only has one y value.

Very similar here when I use my pen and move it vertically across the graph there is nowhere where I'm hitting the shape twice, I'm only hitting it once therefore d, yes, is also a function.

If you don't remember anything else from this video what I hope you remember is the vertical line test. If a graph passes the vertical line test then it is a function. What I mean by that is if you move your pen and it hits only once then yes it's a function, if it hits more than once, no it's not a function.

I personally kind of like theses problems I think they are not too hard and there is no numbers involved so that's kind of cool.

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