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Definition of One-to-One Functions - Problem 3
Determining if a graph is a 1 to 1 function. So before we talked about graphs being a function and what we implemented was the vertical line test. So we looked and we said is there a vertical line that crosses the graph at any more than one point? If there isn’t we know that it is draw the vertical line and it crosses at only one point we know that is a function.
For 1 to 1 we throw in the for every y is there only one x? And what that tells us is for every y value, so here we would say like y is equal to 4 is the only one x value? For y is equal to 4 in this case that is, but we are also concerned with this for every y value. So let’s look at y is equal to 0.
For y is equal to 0 there’s actually three different times when that occurs. So this is a not a this is a function but it’s not a 1 to 1 function and we know that by the horizontal line test. So vertical tells us if this is a function, horizontal will tell us if it’s a 1 to 1 function. So this one is not 1 to 1 by the horizontal line test.
Let’s look at another graph then, so we already looked at one graph it’s not 1 to 1 you can probably guess what’s coming but we’ll look at it anyway. So here we have another graph. You could do the vertical line test to see if it’s a function which this one is as well. Well if you do the horizontal line test to see if it is a 1 to 1 function for every y value there is only one x. So by doing the horizontal line test we know this is a 1 to 1 function.
So checking if it’s a function vertical lines check if it’s a 1 to 1 function horizontal.