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

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

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Oregon State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

02:51

Sketch the graph of the fu…

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02:25

02:24

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02:46

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Sketch the graph of functi…

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So if we want to go ahead and sketch this function three to the X, my suitcase so you can see how I already have number 13 on here, which is just three to the X and other than just plug it in some random numbers and hoping we get, like a decent kind of sketch of it. What normally is a good idea is to sketch the parent function, which in this case is just going to be three to the X. And then you can use that along with some transformations to just kind of boot. Strap yourself to the new ground because no sort of here on the left were starting with FX and then on the right. This is going to be while it's f of X, and then we have experience to is set of X, and then we're adding three on the outside. So what this does if we subtract two on the inside of the function, that is going to be a shift to to the right, and then if we add three on the outside, that's still going to be a shift. But now we're shifting three so we could just take all these points and then kind of make the shift. So negative to become zero negative. One becomes one zero becomes to one, becomes three and two becomes four. And then all of these were just going to add three to it. So this would be 3.1 repeating 3.3, repeating 46 and 12. So these are going to be the point. You're going to end up floating down. Um, and again, you could also just do this directly from the ground. So just one to over 12 Oh, 12 over. 123 Uh huh. And then here, 12 over. 123 up. 123 And then here to over 123 and then this point. Um all right, I just did that one. This 10.2 over and then three. Uh huh, Which should be around like, here. And then the next one, uh, two over and then three of which would be something like that. And then we can just go ahead and connect these. So one thing you might notice is on the left side. All the values are getting very close to zero for the blue function or apparent function. So if I'm adding three to all of those, then the values are now going to be getting very close to three instead. So that is how this graph would end up looking now. Um, yeah. So using this normally is a better way of going about it, as opposed to just plug it in random points. And especially since we've already done number 13, we might as well use it to help us here.

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