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

$$y=3^{x-2}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

McMaster University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:48

Sketch the graph of the fu…

01:55

02:00

02:25

02:51

02:58

03:00

02:46

02:15

02:08

03:13

Sketch the graph of functi…

03:01

01:52

00:35

So if we want to sketch, um, this graph over here we have on the right side, you might see how I have, actually, what number was this from me? And I think it was number 13, Um, where we graph just three to the X, which is really close to three to the negative X. So the only real difference that we did between these is we took our X value, and then the X value became X minus two, as you can kind of see Or maybe I should say, it went from ffx two f of X minus two, and you might recall, just from transformations. This means we're going to shift to to our right, so our values on the right side are going to stay the same. So our outputs, so, like, this is still going to be 0.1 repeating this is going to be a 0.3 repeating. This is still going to be one. This is still three, and then this is nine. But these X values are getting shifted over to so negative to become zero negative. One becomes 10 becomes to one, becomes three and then two becomes four. So this is a way you can just use some transformations that we would have learned before, as opposed to just arbitrarily plugging in some numbers into this. Um, yeah. Now I'm gonna go ahead and just graph these in green. Or you can just think about it again. As and we're shifting all these points to to the right. So it would be 12 12 12 12 And then 12 And then on the left, you can see how it's still just going to be getting really close to the X access. So this one in green will be our why. And again, you could still just go ahead and plug in, um, a bunch of different values and it would give you a pretty decent sketch of it. But since we've already did the work and one of the previous problems 13 or you can released think about doing it that way. Um, it's a little bit more Matthew than just, I'd say, plugging in arbitrary numbers

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