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Sketch the graph of the function defined by the given equation.$$f(x)=\frac{4^{x}}{3^{x+1}}$$

ANSWER IS GRAPH

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Missouri State University

McMaster University

University of Michigan - Ann Arbor

Lectures

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If we want to sketch this curve here, the first thing we can go ahead and do is actually rewrite this little bit just to make the numbers little bit easier for us to plug in. So in the denominator, I'm gonna first rewrite that as three x times, three to the first and then notice. Since four x and three X have that same power, this is just going to be one third times for over three raised to the X, And now we can plug our inputs into this here. I don't make it a little bit easier to work with. So let's go ahead and do that. So I'm just gonna be plugging them into this. So it would be one third times one, which is just one third. So that's about 0.3, um, which would be around here or so, uh, now we can go in and plug in one, so that would just be one third times four thirds, which is four nights, which is going to be just 0.4 repeating. So we're not really making much progress here. So instead of doing two, let's actually give a bunch of numbers and let's maybe do like six. So where is that? So 123456 So somewhere around here, But we play in six. That would be one third times four thirds race in six. And I'll just put that to my calculator, and that's about 1.87 So we're still really not making much progress. So then let's do maybe, like, 10 out here. So 10 is so 789 10. So that would be around, like, here. And if we do that, So one third times four thirds race 10 is approximately 5.912345 pretty much at six. Um, yeah. Then I'll just kind of leave it at this. Actually, let's just do, uh 11, 12, 13 just cause that would be like our last one over there. So if I plug in 13, so just be one third times four thirds to 13, which is approximately, uh, 14. Okay, So 123456789 10, 11, 12, 13, 14. And we can just go ahead and connect all of these on the right side. So it should look something kind of like that on the right side. Uh, and now, since all of these numbers are already kind of small, um, you can see how on the left there just going to keep getting smaller, smaller. So we actually don't even need to plug anything in because we know she's going to keep getting closer and closer to the X axis, and so then this would be our sketch of that.

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