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

ANSWER IS GRAPH

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Missouri State University

Oregon State University

Baylor University

Lectures

02:22

Sketch the graph of the fu…

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00:16

Sketch the graph of functi…

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03:48

Sketch a graph of $y=f(x)$…

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Sketch the graph of each f…

So if we want to go ahead and grab this function here, since they don't really give us many techniques on how to do this, we just go in and plug in some numbers, especially since they just want us to sketch it. So I'm going to start with X is equal to zero, so there'll be 4 to 0, which is just one. So that would be here if we plug in one, that's just four to the one which is four, as that would be 1234 and then we have four squared, which would be 16. And then I believe 16 would be, like, way off the page, like up here somewhere special. I need to get this down a little bit. And, uh, so 14, 15, 16. So, yeah, I think 16 would be maybe around here somewhere. So now we just go out and connect these. I think so. Now we can plug in the negative, so it would be forward to the negative one, which, remember, anytime we have a negative exponents, we're really just going to be reciprocating it. So it's 1/4, which is the same thing is just 3.25 Also, that would be maybe around like here, and then we would do four to the negative second, which would be 1/4 squared again. Negative exponent means to reciprocate. And then that would be 1/16 and 1/16 is zero point 0625 which again would be very close to the X axis. So now notice Over here as we're drawing, we're getting very close to the X access. And we know anytime we have something in the form of A to the X, then it should on one side just get very close to the X axis. And so in this case, it just happens to be on the left side. So it looks something kind of like that. So this would be our graph of this function and now something you could do If you remember some of the like reflections properties, we can look at the previous problem. So this is what we did in that previous problem. Actually make this bigger. So this was four to the negative X. So if we wanted just four to the x notice the way I can inter convert between these is by doing f of negative X is equal to four negative negative acts like this, which gives us or to the X. And this here is telling us we reflect across the Y access so that we could just take these points and reflect them across our ex access. And you can see how this actually matches up pretty much, um or actually should match up exactly with what we did down here the first time. So, I mean, we don't need to necessarily do that, just trying to tie it in with some of the things we've done before. So yeah, I mean, this is probably what they expected us to do, but you can also do that other way as well to kind of get the same graph, especially if you've done the previous problem.

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