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Problem 14 Easy Difficulty

Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3.

$ y = e^{\mid x \mid} $


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Video Transcript

We're going to make a rough sketch of Why equals e to the absolute value of X And let's start by looking at y equals E to the X, our basic exponential growth function that would look like this. Now what happens when we put those absolute value signs in there? I decided to kind of explore with some points. So if we were finding if X was one, we would be finding each of the first. If X is negative one, we would take the absolute value of negative one, and we would still be finding each of the first if X is to, we would be finding it of the second. But if X is negative two, we would take its absolute value, and then we would find each of the second. So what we're going to notice is that the negative X coordinates have the exact same. Why coordinates as their positive counterparts. So what we'll see is what we normally have as the positive part of the graph for the positive X values is just going to be reflected across to the negative side