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. 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. If a graph passes the vertical line test then it is a function. If you don't remember anything else from this video what I hope you remember is the vertical line test. 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. So this case yes it's a function because that x value only has one y value. 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. Here is a couple that are a little bit different when you use your vertical line test down here. That again means that x has two y values, not a function. In this case, we need to remember that all numbers added to the x-term of the function represent a horizontal shift while all numbers added to the function as a whole represent a vertical shift. Vertical oh-oh! You can see your pencil hits places where your vertical line crosses the graph in more than one place. Again, we will use the parent function x 3 to find the graph of the given function. Let's try this next graph use your pencil and make sure it's vertical and not horizontal. 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. Suppose you know what the graph of a function f(x) looks like.
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. Transformations after the original function. And you'll see in this graph there's like tons of places, check it out.
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. Think of this like your pencil this is a big pencil. A mathematical function is a formula that takes an input, x, applies a set of calculations to it, and produces an output. 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. Usage To plot a function just type it into the function box. You can also save your work as a URL (website link).
#Function graph full#
It's using what's called the vertical line test. Function Grapher is a full featured Graphing Utility that supports graphing up to 5 functions together. 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. 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.
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