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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

Campbell University

Baylor University

Lectures

03:27

Sketch the graph of the fu…

03:31

00:16

Sketch the graph of functi…

00:43

03:48

Sketch a graph of $y=f(x)$…

00:37

Sketch the graph of each f…

So if we want to graph for to the negative X since they really don't give us many techniques on how to do this, you know, the first thing we can do is just go ahead and plug in some values. Um, so these are the ones I would think would be pretty nice to just go ahead and plug in, so I'll just start with zero. So we have four to the zero, which ends up being one because here, to the anything is one. And so we would have that point there to start. Then, uh, we've been plug in once. That was us four to the negative one, which is the same thing as 1/4. Because, remember, negative power means reciprocate and then 1/4 of just 0.25 So that would be maybe around, like, here or something. And then if we plug into that would give us four to the negative second, which would again be won over four squared. We reciprocate due to negative. That would be 1/16, which would be equal to zero point 60.625 Okay. And then that woman would just be, like, really close like that. And now, since on this side the values are getting very close to zero, remember, anything to the X Power will never end up being zero. Or I should say, any non zero number raised to a power will never be zero. So that means it's just gonna get really close to the X X is kind of like I mean, not like that. But, you know, it should be getting closer and closer. Now, let's go ahead and find some points on the left side. Uh, so this would first be well, if I plug a negative one. The negatives cancel. So just before to the one which is just four. So at negative one, we have an output of four. If we plug in negative to that would be four squared, so just multiply it twice. 16. Um, so that would be 456789 10, 11, 12, 13 14. I don't know. Let's just say it's like, kind of up here. So I was like, off the page, and then it would look something kind of like that. So that would be our graph of this function

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