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Sketch the graph of the function defined by the given equation.$y=f(x)=(1 / 4)^{x}(\text { compare with Exercise } 15)$

See Exercise 15

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:32

Sketch the graph of the fu…

02:22

03:27

03:04

02:59

Sketch a graph of $y=f(x)$…

00:42

In Exercises $15-20$ , ske…

02:17

Sketch the graph of each f…

00:37

So if they want us to sketch this, I'm just going to plug some values into the start here and then plot those downs. They really don't give us many options on, like how to go about this yet. So first, if we plug in zero, there'll be 1/4 20 Remember anything to the 1/4 is going to be one. Then. If we plug in, want to be 1/4 race to the one which is 1/4 and that's just 3.25 So that would be somewhere around here we plug into would be 1/4 squared, Um, then we can go ahead and distribute that power should be one squared over four squared, which is just going to be won over 16, which would be equal to 0.625 So you can see we're getting, like, really close to it now. One of the things is if we have a exponential function, normally we're going to get really close to the X axis on one side or the other, especially when it's just like some number to the power of X, and in this case it looks like it's going to be on the right side. So we would just get really close to the X axis like that. And now we come over here and plug into other numbers so we would end up having 1st 1/4 race to the negative. First power. Remember what this is? It reciprocates everything on the inside of it. So this would turn into 1/4, which would be the same thing as just four. So at negative one we have an output of for And then if we were to go ahead and do that for negative too. So first it reciprocates the inside, so we get 4/1, but now it would be squared, and then we square both. So four squared is just 16 1 squares, one. So just be 16. And then I think this actually comes off the page. So it should be somewhere up here. If I were to kind of counted out, then we just connect everything onto the left side. So it looks something kind of like that. Um, now, they wanted us to compare this with number uh, 15. I believe. And I actually have 15 right here and actually let me zoom out little so we can kind of, oh, para little bit easier so you can see how these graphs are pretty much the same, or at least as much of the same as my poor handwriting can do. But the thing that you can really make note of is how these inputs give the same output. So what they're trying to kind of like lead you towards is saying that f or not four to the negative X is the same thing as 1/4. Race to the X. So this is kind of like the observation, um, that it looks like they're trying to get us to make

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