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Sketch the graph of the function defined by the given equation.$$f(x)=10^{x} 4^{-2 x}$$

ANSWER IS GRAPH

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Missouri State University

Campbell University

University of Michigan - Ann Arbor

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before we actually start trying to just plug in random points for this, which is one thing we could do. We could actually rewrite this to make it look a little bit prettier and make the numbers a little easier for us to plug in. So that's what I'm gonna do. So first, this sport of the negative two x I'm going to write it in the following way. So it's going to be one over, um, or squared. And then I'm going to pull that power of X out. And so that's going to be 16 and then knows how both of these have a power of X. So this would be 10/16 raised to the X, which is going to be the same thing as 5/8 raised facts. So now if we come over here and just erase this now, we can just go ahead and plug numbers directly into here instead, as opposed to like plugging in to things and then multiplying everything to go. So this is just a little bit easier to plug in. So if we plug in zero, that's first just going to be one. If we plug in one that's just gonna be 58 and 58 is approximately, um, are. Actually it's exactly equal to 0.625 And then if we plug in two so 58 squared, that should be approximately 0.39 So let's just go and plug those ends. We have one 0.65 So that would be around here and then 0.392 So something like that So you can see how, on the right side we're getting closer to the X axis. And since it's just a number two of power, we know that it should be getting very close to the X access like that. Now we can go ahead and just plug in the numbers on the other side. So we have 58 the negative first, which will just be hate fifth, because it reciprocates so that the 1.6 So that would be somewhere around here if we plug in negative too. Um, that is going to be so five eights to the negative. Second again, remember, we just reciprocate. So would be 8/5 squared, which should be 2.56 So somewhere around here and Now we probably need to plug in a couple of other values. So what I'm gonna do is just come down here and plug in, like negative or because maybe after we do that, it will make it a little bit larger. So it would be 58 raised the negative fourth, which remembers the same thing as eight if raised to the fourth. So that would give us something around 6.5. So two, um, 3456 So something around here and then let's just try, like, negative six to see what we get after that. So that would be 58 raised to the negative six, which is something around 16.7. So if this is, uh, six or so here than that 789 10, 11, 12, 13, 14, 15, 16. So, yeah, it would be kind of way off the page, like up here. So now we just go ahead and connect these and it will look something kind of like that. So that would be the sketch background again. You could just plug the numbers in. But rewriting in this form makes it a little bit easier to just actually get the numbers out

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