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Problem 22 Medium Difficulty

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 = \frac{1}{4} \tan (x - \frac{\pi}{4}) $

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to graft. Dysfunction will start by looking at the graph of the standard function y equals tangent X. And I'm just going to grab a small bit of the tangent function. So we know that it has a vertical Assen towed at Pi over two and another one at negative pi over two in between, we have pi over four negative pi over four. And so the standard graph looks something like this. Let me put in a couple of points here. We have a height of one and a height of negative one. It was something like, Let's try that again. Took you to make it go through the appropriate heights. Something like that. Okay, now we have those repeated over and over and over again with vertical Lassen totes in between. So there would be another one over here and so on. Okay, Now, what are we going to do to that? Well, we are going to shift it to the right for and we're also going to shrink it vertically. Make it 1/4 is tall, so let's go ahead and make a graph for that. Okay? Shifting it to the right. Didn't mean to say for him and to say pi over four, shifting it to the right pi over four. Let's do that by shifting our vertical Assen totes. Okay, The vertical Lassen tote that was previously at negative pi over two is now at negative pi over four and the vertical sm the ass and tote that was previously a pi over two is now at three pi over four. Okay, now, halfway between those, we have a zero. And then instead of having points at a height of negative one and one like we did earlier, they're going to be at a height of 1/4 and negative 1/4 because of the vertical shrink. So it's going to look something like this, and we would repeat that to the left and the right. There will be more of those.

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