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Sketch the graph of the function defined by the given equation.$$y=f(x)=3 e^{-2 x}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

The Number $e$

Missouri State University

Oregon State University

Idaho State University

Lectures

01:29

Sketch the graph of the fu…

01:27

01:17

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00:14

Sketch a graph of the give…

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02:15

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02:24

01:55

03:00

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02:00

02:25

eso Our task is to graph three e to the negative two X. Um and the best way to do this is to go through the reflections. Um, uh I mean, I should say transformations, but the first thing is that we have a reflection, um, over the y axis. But aside from that, there's actually two stretches and dilation. Um, I said that wrong, but I think you get my point is there's a horizontal shrink or compression of one half, Um, and a vertical stretch by three. Um, now the very first thing, If if you wanted to, you could actually make a table values. I know some t's. Yeah, teachers do this, but actually makes more sense. If you were to have X values of, like, negative one half zero and then positive one half. And I think that should be enough points for you to figure out what the correct answer is because if you plug in zero and for X well, anything to the zero power Well, they one times three would be three. So at the very least, everybody should have a graph that goes up to zero three. But there's a reason why I chose values like negative on half, because if I dio negative one half of negative, so you get positive. One s o e to the first powers E times three would be three e. I don't know exactly what this is without a calculator, but he's about 2.718 Eso if you triple, that's pretty pretty large. The point I'm trying get is 345678 Now I know it's smaller than nine. Let's say this is negative one. Um, you know, we get approximation somewhere up here, whereas if you did a value like this one, you get beat to the name your first power, which would be three divided by e, which is a little bit larger. So if that's one, it's a little bit larger than why value of one. Um, but anyway, exponential decay is what we're looking at. Um, and the graph would look something like this. Um, and all of my transformation still hold true.

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