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Numerade Educator

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Problem 7 Easy Difficulty

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

$ y = 2^x $ , $ y = e^x $ , $ y = 5^x $ , $ y =20^x $

Answer

All of these graphs approach 0 as $x \rightarrow-\infty,$ all of them pass through the point $(0,1),$ and all of them are increasing and approach $\infty$ as $x \rightarrow \infty$. The larger the base, the faster the function increases for $x>0,$ and the faster it approaches 0 as $x \rightarrow-\infty$. Note: The notation " $x \rightarrow \infty "$ can be thought of as " $x$ becomes large" at this point. More details on this notation are given in Chapter 2.

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Video Transcript

okay for this problem. We're using a graphing calculator and we're graphing The four functions. Why equals two to the X Y equals E to the X Y equals five to the X and y close 22 the X, and we're going to see how they compare. So for window dimensions, I'm going to go with X Man is negative. Five X max is 10. Wyman is negative 50 and why Max is 500 and window dimensions can vary. You can just play around with it until you find something you like. So let's take a look at these graphs. Okay? So minor color coded, which is really handy, and the blue one was why equals two to the X. The red one y equals each of the X. The black one y equals five to the X and the pink one y equals 22 the X. So they're all exponential growth. That's what they have in common because they have different bases, they have different steepness and they grow at different rates.