anonymous
  • anonymous
Find equations for the horizontal or oblique asymptotes, if any, for each of the following rational functions. #1) F(x)=5/x-1 #2)F(x)= x^2-4/x+2 #3) F(x)= x+2/x^2-9 #4) F(x)=3x^2+1/x-2 Can you please show your work so I can understand how you got the answer. Thank you! I will definitely award medal
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
DebbieG
  • DebbieG
Do you know the rules for the horiz asyp? You just compare the degree of the num'r with degree of the den'r. If degree num'r
DebbieG
  • DebbieG
If degree num'r>degree den'r, that's where you get an oblique asymptote. In that case, you have to do the division, e.g., divide the num'r by the den'r. Whatever you get as the quotient is your equation for the oblique asymptote. You can ignore the remainder, because that part will -->0 as x gets large.
anonymous
  • anonymous
This is my answer for 5/x-1 VA: x=1 HA: y=0 Y-intercept: -5 No x-intercept Now how would I graph this? Thank you so very much for that help debbie

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

DebbieG
  • DebbieG
Good, all of that looks perfect. Put all of those things on the graph first. Then think about some values near the VA. E.g., to the LEFT of 1 (going towards 1, but from values that are less than 1), what is happening to the function? There's a VA there, so we know it's "blowing up"..... but is it blowing up to +infinity or to -infinity? (Think about the sign of the function when x<1). This will tell you the behavior as it approaches that VA from the left.
DebbieG
  • DebbieG
Ask the same question as you approach it from the right, e.g., as you get CLOSE to x=1 from from values where x>1.... what is the sign of the function? That tells you "which direction" it is blowing up.
DebbieG
  • DebbieG
You also have the y-intercept, so of course plot that. You can find a couple of other points if you want, but really.... if you have a "feel" for what the function looks like, once you have the asymptotes and any intercepts on the graph, you can get a pretty good sketch.
DebbieG
  • DebbieG
Also if you happen to be familiar with the graph of \(y=\dfrac{1}{x}\) notice that this is just \(y=5\cdot \dfrac{1}{x-1}\) which is a horizontal shift, and a vertical stretch, of \(y=\dfrac{1}{x}\) :)
DebbieG
  • DebbieG
Be careful on #2. It's not in lowest form. :)
anonymous
  • anonymous
|dw:1377776688627:dw|
DebbieG
  • DebbieG
Reduce to figure out what the graph LOOKS like, but you still have to leave out of the domain, any x-values that make the ORIGINAL (not reduced) expression undefined.
DebbieG
  • DebbieG
That's only half of the graph, you know? (Just making sure you know you aren't finished yet). And you need to get the graph over closer to the VA. Right now it looks like you have x=0 (the y-axis) as a vertical asymptote.
DebbieG
  • DebbieG
|dw:1377776809757:dw|
anonymous
  • anonymous
|dw:1377776852625:dw|
DebbieG
  • DebbieG
Yes, that point would be y=-5. And what more is everything that is happening for x>1. :) You haven't shown anything in that part of the domain.
anonymous
  • anonymous
So that's the complete graph?

Looking for something else?

Not the answer you are looking for? Search for more explanations.