Dis0 tina the horizontal and vertical asymptotes of A) (x^2 + 3x-10V(5xn2 5x 10)B) (4x-2)x+3ylx-3)x-1)...

a. Identify the horizontal asymptotes (if any). b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. $$ p(x)=\frac{5}{x^{2}+2 x+1} $$

This problem is asking us to fund all horizontal and vertical Assen totes. If Eddie okay, we've been given five over X minus two is equivalent to our backs. The first thing we know is that X equals two is our vertical ascent toe. And the reason why is because it's zero of the denominator. That is how you find the vertical asked conversely, why equal zero is the horizontal awesome toa because we seek. But zero is less than one wife whose ear is the horizontal ascent took. In other words, if we're looking now at the numerator instead we would see this. This is where we would see the horizontal line. Obviously this is just one of the axes, right? This isn't anything different than just writing out the normal X and Y axis.

In the question. It is given that function F X because two experts fire upon access school, we found the limit. Extent, stream feeding explores fire upon access quail. That means it is in 50. So we can see that it has no horizontal. Yeah, as imports. Yeah. And we can see there for the function. Jurors of barometer. Okay, exit points to zero. So we can see that at the request to zero denominator zero. But new reader attacks cause usually does not cost to you so we can see that consequence to zero Mhm vertical his dimples. I hope your nation These are the answer. Thank you.

In this problem, we are given the function of F of X. And we're asked to find a few different things. So the first thing we're looking for is X intercepts. So whatever we're hitting an X intercept, that's where Y equals zero. So we can solve this by looking at zero equals five X squared minus three Over two X. to the 5th -3 x plus two. And that's gonna look daunting if you're looking at it this way, what Think about the fact that for why we're zero? We want this to be zero over some number If our denominator zero is just undefined. So really we're looking at 10 equals five X squared minus three. So we'll do some algebra here at R three over then we'll divide five. So we have 3/5 equals X squared. And now we just want to take the square root, We have x equals square root of three over five. And if you put that on your calculator you can get an estimation and this is positive and negative So it's about positive and negative .7746. So that's gonna be your two x in ourselves. And next we're looking for vertical ascent tops and that's where our functions undefined or where the denominator equals zero. So we're looking at zero equals two X. To the fifth minus three X plus two. And you're going to use your calculator to help you solve this year. So we do that. We get x equals native 1.23297. That's our vertical S in tow. And we're also asked for a horizontal a symptom and That one is a little more difficult to remember and to do. So what we do with that? So we have our original function F. Of X. We'll write this out first. And what would do to find a horizontal S into? We take the highest powered variable. So on the top we have five X squared. And in the dominator our highest exponents is the five. So we have to accept the fifth. And we simplify this so we have five over to execute and you think, okay, so if it's bottom heavy or the variable is only left in the denominator, consider the fact that as X gets higher and higher, our denominator gets bigger and bigger. So we approached zero. So this is just me, zero. Why Go? zero is going to be our horizontal ass into now that we have all this information, whereas to graph this function and this can be a little tricky. But with the information we have we can at least get a rough idea of what we're looking at. So we have X intercepts, put one there at 0.77 so we'll call that approximately there and we have that in the negative too. So That's gonna be a zero. Not race these. So we don't get too confused. All right. And we have a vertical as in tow. But why X equals negative 1.23 three. So, we'll put that about here And we have horizontal asientos at y equals zero that's here. Okay? So what we're looking at here, we're not going to want to cross this. So we have some kind of function over on this side of things. And if you want to just plug in a number into our functions, sometimes that can help you. So if you do that, you see it gets more negative. So it's going to kind of like that because we have our ascent at Y equals zero and X equals negative 1.2. And if you graph negative one or plug into your function, you'll see that it's a positive number. So we're going to have something starting up there and we know we cross across the X axis here and we know there's another zero here. So we come up through, but then we still have an awesome tote at Y equals zero. That's going to come back down. It's just going to approach zero like that. So, again, probably not going to be your prettiest sketch of a graph. But with the information we have and plugging a few points, you can get a general idea of what you're looking at.

Now This time they give us the irrational function. Are objects is equal to you? I've excuse over Waas Teaneck squared. Fine. Well, what about horizontal? I know where they are. So how do you get the horizontal Assam? All right. Both of the pond on meals on the numerator and denominator with single tree. Yeah, their lawyers Binomial terry slipped their cooperation. Hey, that's five in one generation. Numerator is over the two nominees over one. So we have a Y eyes of why is it our hotline plotting to now let's look at essential vertical assets. That's when the denominator is zero. So we're gonna factor that polynomial again. My infamy. It's fine. That's about the discriminative that b squared. So four minus four c, this is less than zero has no real solution. So there's only one possible zero under denominated. Well, and this zero X is equal to zero. Gives rise to a critical asset. Okay, the sirah has already