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Problem 74 Hard Difficulty

Graph the given functions on the same screen. How are these graphs related?

$ y = \tan x $ , $ \frac{-\pi}{2} < x < \frac{\pi}{2} $ ; $ \tan^{-1} x $ ; $ y = x $

Answer

see explanation

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Video Transcript

okay we're using or graphing calculators were going to go to the y equals menu, and we want to graph y equals tangent of X as well as y equals inverse tangent of X as well as y equals X. Now let's go to mode and make sure our calculator is set to radiance. And if not, you want to change it to radiance. And now let's go toe window. And we want our X values to go from negative pi over to two pi over to so weaken. Type that in. Actually use your pie button for accuracy there to have negative pi over two pi over two and then for the y values. We could have different ideas for this. I'm just going to go with, say, negative 5 to 5 and if I don't like it, I can change it. So let's look at the graph. Okay, so if you press trace, you'll be able to tell which color is for which graph. So the blue one is for the tangent graph. The red one is the inverse tangent graph, and the black one is the line y equals X. So what we noticed is that the tangent and the inverse do look like reflections of each other across the line Y equals X, as in verses should.

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