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Sketch the graph of the function defined by the given equation.$$f(x)=\frac{5^{2 x-1}}{6^{3 x+2}}$$

ANSWER IS GRAPH

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Oregon State University

McMaster University

Lectures

01:57

Sketch the graph of the fu…

06:24

02:10

Sketch the graph of $f$.

02:02

02:13

Sketch the graphs of the f…

00:36

Sketch the graph of $f$

00:28

00:16

02:49

00:24

So before we actually try to graph this, what I'm gonna do is rewrite this a little bit just to make it so it's easier for the numbers to plug in. So first in the numerator, we can break this up into the following way so that apply to the to express one. Well, that's first going to be five to the two. X times five to the negative first, and then the dominator would be 6 to 3 x times six square. Now, um, this five to the two X we can actually rewrite as five squared raise the X so that is going to be 25 to the X and then by to the negative one, it's just gonna be 1/5 and then three or 62 to 3 X. Every right is six to the three. Raise the X and then six cute is 216 would be 216. Race of the X and then six square is just going to be 36. Yeah, Now we can go ahead and pull this common power effects, which is going to give us 25 over to 16. Raised to the X and then 1/5 divided by 36 is going to be won over 180. So we can instead plug numbers into this. And this is a little bit easier to plug in than, I mean, everything we had going on over there. So first, if we plug in zero, that first part just becomes one. So just be won over 108. So I mean, like, that's really close to the X axis. Um, if we plugged in one and actually you can see if we probably like 12 and all that, it's really not going to make too big of a difference. Um, so what I'm going to do instead is just plug in maybe, like, five. So five and 10. So let's say we're five antennas. So 12345 So five is here. 6789 10 and then I'll do the same thing over here. I'll do negative five and negative 10. That was the 123456789 10. So when we plug in five into this and I'm going to plug this directly into my calculator, um, that's going to be, like, 1.2 times 10 to the negative seventh. And if I plug in 10, it gets even smaller. So just make two times 10 to the negative 12. So you can see how, on the right side these numbers are just extremely close to the X access. Um, And then when we plug in these negatives over here, So negative five. Actually, that gets really big Really quickly. So maybe just doing, like, negative one and negative two are going to be okay, So negative one was actually still extremely small. Um, this is going to be 0.48 So, you know, maybe not even slightly above. And then, um, negative to still isn't much larger. So actually, let's do, like, negative re instead. So if we do negative three, that gives us something around three point five. So 23 123 And then around here and then negative. I was too big. And then negative four is also way too big, because negative for is around like 30. So you can see it just gets really big really quickly after this point, So it just looks something kind of like this and then just kind of explodes after them. So this would kind of be a somewhat sketch of our graph here.

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