Question

Find the horizontal or oblique asymptote of f(x) = 2 x squared plus 5 x plus 6, all over x plus 1.

Answer 1

WILL MEDAL AND FAN!!!
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Answer 2

@CheesecakeKitten Bruh..

Answer 3

@mathmale Hi

Answer 4

OfMice: Hi.

Could you please enter your problem statement symbolically (using either the Equation Editor or the Draw utility, below)? It's worth learning how to use those utilities.

Find the horizontal or oblique asymptote of f(x) = 2 x squared plus 5 x plus 6, all over x plus 1.

I'm unsure whether you mean (2x)^2 or 2x^2, for example.

Answer 5

@mathmale 2x^2+5x+6
----------
x+1

Answer 6

@mathmale

Answer 7

@Kenshin hey

Answer 8

@ofmiceparade Hi, do you understand what the question is asking of you?

Answer 9

@Kenshin Yea. I forgot how to do all this over winter break.

Answer 10

you have an "improper" fraction. divide (x+1) into the top to make it a "mixed" fraction
can you do that ?

Answer 11

? Im not exactly sure how to divide that to the top

Answer 12

We are talking about "asymptotes" here, as specified by "horizontal or slant asymptote." OfMice: Before we proceed, please share what you think "asymptote" means in this context.

Answer 13

it is hard to explain quickly if you don't know how (though I suspect you are supposed to know because that is how you solve this problem)
see https://www.khanacademy.org/math/algebra2/arithmetic-with-polynomials/long-division-of-polynomials/v/polynomial-division
for a quick review

Answer 14

An asymptote is a line or curve that approaches a given curve closely

Answer 15

Actually, asymptotes are all straight lines, and graphs approach their asymptotes, rather than the other way around.

Answer 16

Oh

Answer 17

What would be the equation of the horiz. asympt. of \[y=\frac{ x^2-4x + 5 }{ 2x^2 }?\]

Answer 18

Have you found horiz. asy. before? If so, how?

Answer 19

...

Answer 20

I have no idea.

Answer 21

I haven't done this in over a month

Answer 22

Have you thought of researching "long division" on the 'Net? or, if you have a textbook (which I hope you do), have you looked up "long div." there?

Answer 23

I could explain this whole problem in a few minutes, but that would cheat you out of learning how to research info by yourself.

Answer 24

I just need help with question

Answer 25

I don't know where to start

Answer 26

Suppose you let x grow larger and larger in the following:

\[y=\frac{ x^2-4x + 5 }{ 2x^2 }\] As you do this, y will approach what value?

Answer 27

Division?

Answer 28

I'm clueless to what you just asked.

Answer 29

When you have an improper fraction of algebraic expressions, after you manipulate it into a mixed fraction using long division, you will get a quotient and may get a remainder term afterwards which stays above the denominator. the quotient value is your horizontal or oblique asymptote, by horizontal it just means it is a 'y = constant' value, by oblique it means it's slanted like a diagonal line or curve in other cases (@mathmale which I think it can be a curve still not just line if say..you get y=x^2 as the quotient before the remainder)

Answer 30

I needed to test your knowledge of "asymptotes."

Without that understanding on your part, we'd have to start from scratch. You say you haven't done this type of work for a month or so...which implies that you had some familiarity with it in the past. What stops you from going back to review that material?

Answer 31

Take another look at:\[y=\frac{ x^2-4x + 5 }{ 2x^2 }\] and drop some terms:\[y=\frac{ x^2}{ 2x^2 }\]

Answer 32

I'm trying to finish my first semester. This is one of the last assignments. I just want to finish.

Answer 33

Now, what happens to y as x grows "very large?"

Answer 34

What do you even mean by that? I don't know. It changes?

Answer 35

\[y=\frac{ x^2 }{ 2x^2 }\]

Answer 36

sorry, my previous entry was very hard to read. This is what I meant (see above)./

Answer 37

Okay. Y = x^2/2x^2

Answer 38

Yes. I'm asking you to determine what y value this expression approaches if x keeps growing larger and larger.

Answer 39

The y intercept?

Answer 40

No, I'm asking you for a numerical limit. "As x grows larger without bound, y=(x^2) / (2x^2) approaches the value _______ "

Answer 41

y^2

Answer 42

What is (x^2) / (x^2)?

Answer 43

Asymptotes are usefun in graphing functions. For example, in the function we've been discussing, if x grows larger without bound, y approaches the limit (1/2). thus, the horizontal asymptote is a line described by y=1/2.

Have you encountered this information / material before?

Answer 44

x times x over x times x

Answer 45

^useful, not usefun.

Answer 46

Yes, and what is x times x over x times x?

Answer 47

theres no number..
WHAT DO YOU MEAN

Answer 48

its an X

Answer 49

this is algebra. x/x = 1. (x^2) / (x^2) = 1.

Answer 50

What I am doing here is trying to introduce the concept of "asymptote." This concept seems to be either very new or just strange to y ou.

If that's the case, this problem is not going to make any sense to you.

I'm willing to spend time with you if you truly want to learn this material, but as a matter of principle, I won't be giving out answers. My goal is that you learn enough so that you can find your own answers properly.

Answer 51

oh

Answer 52

yea

Answer 53

Here is the original question:

"Find the horizontal or oblique asymptote of f(x) = 2 x squared plus 5 x plus 6, all over x plus 1." I'll go so far as to tell you that there is an asymptote here, and that it's a horiz. asympt., not an oblique (slant) asymptote.

What form would the equation of a horiz. asymptote have? It's just a horiz. line.

Answer 54

y= something since theres no x point?

Answer 55

\[\frac{ 2x^2+5x+6 }{ x+1 }\]

Answer 56

I already wrote that but now what?

Answer 57

That "something" would be a numeric value.

Look at the expression I've just typed in, above.

the numerator has the order 2 (as in 2x^2) and the denominator has the order 1 (as in x+1).

if you divide x+1 into 2x^2 + 5x + 6, you get the following:

y becomes approximately equal to 2x + 3.

This has the form y=mx + b and is therefore a straight line (asymptote line, slant asymptote).

Answer 58

If you were to graph both the given function and this asymptote line, you would see that the curve approaches the line (like a horse appraoching a fence almost parallel to the fence).

Answer 59

Do you have a graphing calculator?
If so, would you be able to graph the function y=(2x^2+5x+6) / (x+1)?

Answer 60

Yea hang on, lemme get it

Answer 61

I graphed it

Answer 62

Can you describe what your graph looks like? Is it a continuous curve or is it a curve with two separate parts?

Answer 63

Thats it

Answer 64

Please see the following. I've used an online utility to graph the same function. My result agrees with yours.

http://www.wolframalpha.com/input/?i=%282x%5E2%2B5x%2B6%29+%2F+%28x%2B1%29

Answer 65

Now imagine a straight line drawn diagonally just above the left half of the graph and just below the right half of the graph. The curves practically touch the straight line as you move away from the origin.

THAT is the "slant asymptote."

Its equation is y=2x+3.

Answer 66

Oh Okay. Thanks so much!

Answer 67

time to wrap this up. But first, any questions about what we've done here?

I

Answer 68

@mathmale Nope. Thanks for spending like 30 minutes on me. I faned and medaled you

Answer 69

I strongly encourage you to look up and review terms such as "asymptote,", "slant asympt.," horiz. asy. and vertical asy.

Answer 70

...and you should know how to find them.

thank you for your patience and perseverance and for the medal / fan. Take care!

Answer 71

Eh, im never using this in my real life. But thanks tho.

Answer 72

Perhaps not, but learning HOW TO LEARN is extremely imkportant.

Answer 73

Its a bit more difficult when you don't care about the subject. I rather learn language

Answer 74

I've forgotten at least 90% of the subject matter I learned in college. But I'm good at le3arning or re-learning stuff. That's what counts.
Yes, I undrstand: you prefer verbal rather than math'l or scientific learning. That's OK.
Just a preference. and greater talent in one area than in another. Best wishes to you.