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

ANSWER IS GRAPH

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

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Sketch the graph of the fu…

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So if we want to graph this, Um, since we don't really have many techniques to do it yet, we just go in and grab a couple of points normally for any kind of maximum to try and say These are normally good numbers to just use at the start. So let's just go ahead to use these and then we'll go from there first. I'll go ahead and plug in zero, so that would be 3 to 0. And remember anything to the zero is one. So then we just have one on our graph over here. Uh, then if we plug in one, that would be three to the negative one, which is one third, Um and that's just 0.3 repeating. So if we plug that in and it would be probably somewhere about, like here for two, it be three to the negative Second. And remember, if we have 3 to 92nd, that's according to reciprocate it to be won over three squared, which then ended up becoming 1/9 and one. Number nine is equal to 0.1, repeating. So then that would be even closer to the X access and Then you might notice that we would end up with values that just keep getting closer and closer to zero. And we would know at any time we have something in the form of like a raise to the X. We always end up with, like, a horizontal Asato at just zero. So this is going to look something like this as we go to the right. So I'm just going to keep getting closer and closer to the X axis. Now, let's just come over here and plug in some numbers to the left. So, like negative ones, that would be three. Uh, so negative. Negative one. That would just be one. So let's just three. So a negative one, Uh, at that point there. And then if we plug in negative to the negatives again councils, though, just be three squared, which is nine and then so at negative two. So we have 3456789 and then we can just go ahead and connect these here like that. And then that would be our graph with three to the negative acts

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