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Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.

$ y = 1 - \frac{1}{x} $

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Missouri State University

Oregon State University

Harvey Mudd College

University of Nottingham

our goal list. A graph y equals one minus one over X. So I'm going to start by thinking about the graph of y equals one over X. That's our standard reciprocal function. And it looks like this. Okay, now what would we do with this function? What would we do with y equals one over X to get the function we're interested in? Well, im going to rewrite the function I'm interested in in a slightly different way. I'm going to rewrite it as why equals the opposite of one over X plus one. I just rearrange the order of the terms. Okay, So now the next step in the process is what does why equal the opposite of one over X looks like look like while multiplying by a negative one is going to reflect the graph across the X axis. So now it's going to look like this. Now what's going to happen when I add one to that? It's going to shift it up one. So what we just drew is going to be shifted up one. Now what we just drew has ah horizontal Lassen tote at zero and a vertical lassen tote so horizontal Aston todas y equals zero vertical Aston todas X equals zero. So when we shift the whole graf up one, we're shifting that horizontal Assam towed up one as well, and it won't change the vertical Lassen tote. So here's what we get.