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Graph the given functions on a common screen. How are these graphs related?$y = e^x$ , $y = e^{-x}$ , $y = 8^x$ , $y = 8^{-x}$

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Lily A.

Johns Hopkins University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

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Video Transcript

in this problem, we're going to compare some graphs using a graphing calculator. So we go to the y equals menu. We type in the four functions Michael's either the X Y equals E to the opposite of X Michael's A to the X and Y equals eight to the opposite of X. Now, before I look at all four of those graphs at the same time, I'm just going to look at the 1st 2 y equals e to the X and e to the opposite of X. So I've turned off the equal signs on the last two and here we go. Okay, so the blue one is y equals e to the X. That looks like your typical exponential growth. And the red one is y equals each of the opposite of X. These air reflections across the Y axis. Now let's take a look at the other two. So let's turn off the 1st 2 and turn on the last two. Okay, so the black one is y equals eight to the X, and the pink one is y equals eight to the opposite of X notice that these air also reflections across the Y axis So if you replace X with the opposite of X, you reflect across the Y axis. Now let's take a look at y equals E to the X, and why equals eight b x. These are both exponential growth. The one with the base of eight is steeper. And now let's take a look at why equals either the opposite of X and eight Michael's eight to the opposite of X. So these are both exponential decay. The one with the base of eight is deeper, so we had to exponential growth to exponential decay. To that were reflections across the Y axis from one another two pairs.