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Sketch the graph of the function defined by the given equation.$$f(x)=(0.65)^{-x}$$

ANSWER IS GRAPH

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Baylor University

Idaho State University

Lectures

02:01

Sketch the graph of the fu…

02:31

03:00

03:12

00:49

00:35

01:15

01:16

01:32

01:55

02:13

so if we want to grab this, Uh, since I really don't give us too many real options for doing this, we just go ahead and plug in some random values, Uh, and here and then use that. Help us just kind of put them on to the board. So let's just first see what we get when we plug these in. So we get 0.65 races zero, which is just one. So actually, let me do this in green, so it kind of stands out. If I do 1 to 0.65 now, this will be raised to the negative first, which is same thing as 1/0 0.65 And that should be something around 1.53 So negative one and then would be around here. Um, now, if we plug in to 0.65 raised to the negative second and that's the same thing as 1/0 0.65 squared. And that is approximately 2.36 Um, actually, I don't know why I did it over there. I should have been putting it on the right side around here, and then two It's like 2.36 so we'll probably need to plug in a couple other values over here, so I'll just go ahead and plug these in the first, so Ah, negative one. So the negatives are going to end up cancelling out with each other, so it would just be to the first power. So just 0.65 So that is somewhere around, like maybe here. And then if we plug in to our negative to that, just give us 0.65 squared. Uh huh, um, which is around 0.42 25 That is about here. So first, we can go ahead and just connect these like that. And any time we have something like a to the X, remember, it's going to end up getting very close to the X axis. You don't have a lecture on the right side. So here you can see how it's getting closer on the left side. Now I just go in and put like five and 10 down, and hopefully those don't get too big over here. So let's see. So that's, uh, 234 So here is five and then 6789 10. So I'll use these two. Or maybe I should put dots and put like little Astra's just sort of like a marked 678 10 like that. So if I come down here, get me to do that? Yeah. So? So, 5. 10. Yeah. So we plug in five into here, we should get Well, actually, yeah, Tyne is going to be way too big, so I'll just stop it. Five. So five would be 0.65 raised to the negative 50 which would be the same thing as 1/0 500.65 to the fifth. And there is approximately 8.61 So 12345678 And then around here. So then, yeah, if we plug in 10, we end up getting, like, 75 which, as you can tell, will not work very well for my charge. So yeah, look something along the lines here. You could put some more points in between if you want to kind of fill it out a little bit more. But since we're just kind of sketching, I would say this is a good enough graph. They are safe approximately 75. Since I have that down there

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