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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.$y = \mid \cos \pi x \mid$

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to graph dysfunction. Let's start by thinking about the standard function Y equals co sign of X. What does that look like? Goes upto one down to negative one. It has a period of two pi. So the coast and graph in general looks like this. The regular standard Cho sang graph. Okay. And it keeps going forever to the left and the right. That's just part of it. Now what happens if we multiply the X pipe? I What does that do that's going to be a horizontal shrink by a factor of pie? That means it's pi times narrower than it used to be roughly three times narrower. So the period, the width of one cycle used to be two pi. Now the period is going to be just too. We divide the period by the horizontal shrink factor, so the period is just going to be, too. That's roughly three times narrower. Now, I'm not gonna make that perfectly to scale compared to the previous one. I'm just going to put a to here and a negative to here. We still go upto one down to negative one. That didn't change. So roughly here is the graph we have now. But now the final thing we want to do is the absolute value signs. So the absolute value is going to make it positive. Anything that was previously positive will still be positive. Anything that was negative is going to now be reflected across the X axis and made positive. Okay, so I graft was positive for a while. Then it went negative. So that negative part is going to be reflected back up. And it was positive for a while, and then it went negative and that negative parts going to be reflected back up. And then it was positive for a while, So that's what we get.

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