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Sketch the graph of the function defined by the given equation.$y=f(x)=(1 / 3)^{x}(\text { compare with Exercise } 14)$

See Exercise 14

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

Oregon State University

Harvey Mudd College

Lectures

03:02

Sketch the graph of the fu…

03:04

03:12

01:18

Use the graph in Exercise …

02:15

02:08

00:25

01:37

01:55

Sketch the graph of each f…

01:00

Graph the given function a…

03:31

00:30

Sketch the graph of $f$

03:24

Yeah, So if we want to graph this is they really don't give us many ways of graphing exponential functions outside. Just kind of plug in some numbers. And that's just what I'm going to do. Let's come over here and do this. So we have one third rate zero at anything to zero is one. So we have this point here. We plug in one, so we have one third to the one, which is just one third, which is even to just observe 10.3 repeating. So that would be, I don't know, probably somewhere around, like here. And then we plug in two, so that would be one third squared. So we do one third times one third, which is one night, which would be equal to 0.1 repeating. So that would be like, really close to the access now, Anytime we have something where it's like a to the X, normally on one side, it's going to get very close to the X axis. So you can see here how on the right side will be doing that so we could go ahead and connect these points. Is that just how Berg it's really close to the X axis, so it's trying to come up like that, but I don't have steady enough of a hand to do that. Um, now we plug in negative one. So the one third rate negative first power, and then that just reciprocates this. So that gives us 3/1, which is just three. So at negative 11233 And then we plug in Negative, too. So would be one third race, the negative second. So again, it reciprocates it. So it'd be 3/1 squared, and then that would just be nine. Uh, so three, 456789 And then we just go ahead and connect these. And I would say that's a pretty decent sketch if I could draw a smooth line, which I obviously cannot. But now they wanted us to compare this with the one from exercise 14. So I went ahead and already have that up here actually make a little bit bigger. Yeah, So you can see how the graphs here look pretty much the same. And if you actually look at the inputs and the outputs, those also match up with each other So what they're trying to get you to kind of see here is that it looks like three to the negative. X is the same thing as one overact or 1/3. Race to the X. So this is kind of the observation I think they're wanting you to make here.

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