Question

State the horizontal asymptote of the rational function.

f(x)=x^2+4x-7/x-7

Answer 1

horizontal asymptotes are a bit different

where does this equation approach....when x is set to infinity?

focus only on x²/x

so imagine infinty ² / infinity

what does this equal?

Answer 2

Ummmm...Infinity?

Answer 3

correct! I know don't let it confuse you....it really is that simple :)

Answer 4

so....realistically....where would you see a horizontal asymptote? at infinity?

where would you graph infinty? you wouldn't.....so for this example.....there is no horizontal asymptote....but if there was one...it would be at infinity

Answer 5

Okay:) Thanks much:)

Answer 6

I hope that made sense??

Answer 7

Not entirely, but next time I have a question I can just look back on this to see if it will help.

Answer 8

lol okay...but to make it clear

infinity² / infinity = infinity.....a.k.a NO HORIZONTAL ASYMPTOTE

now imagine

x / x
set those both to infinity

you have

infinity / infinity....= ...1 right? any number divided by itself is 1....for this kind of problem...you would have a horizontal asymptote at 1

now imagine

x / x²

set THOSE both to infinity

infinity / infinity ²

since the denominator grows faster than the numerator....the number gets SMALLER and SMALLER until it approaches 0

imagine

1/10....then 1/100,...then 1/1000.....1/10000000000

gets smaller and smaller of an answer right? same thing....for bigger and bigger numbers that you put for x...the answer would get smaller

so in THAT case.....x / x² approaches 0.....so it would have a horizontal asymptote at 0

Answer 9

hopefully THAT helps :)

Answer 10

Yea, That helps more:) Thanks:)

Answer 11

anytime :)

Answer 12

But what if you have something like 9x^2/ 4x^2?

Answer 13

oh and to clarify 1 more thing

when I said "only focus on x² and x

imagine you have 100000000000000000000000.......+ 4x + 3

those 4x and 3....dont do much to add to this number right? so we ignore them...we focus ONLY on the higest degree terms.....but okay....your next question...

Answer 14

so we have 9x² / 4x²

(thank you for pointing out that I missed a part :))

9x² / 4x²

remember when I said

x / x ....would be 1?

so

9x² / 4x²

the x² and x² go to 1

so all you have is

9/4

Answer 15

Well the full problem is f(x)=9x^2-3x-8/4x^2-5x+3, do you still only focuse on the 9x^2/4x^2?

Answer 16

because remember....technically you are dividing

so

9x² / 4x²

x² / x² no matter WHAT x is....will equal 1 right?

so all you'll have is 9/4 left......hang on lemme see what you just said

Answer 17

you are correct :) you only focus on the highest degree terms in the numerator and denominator

Answer 18

Okay, It just confused me that you have this long equation and you only focuse on the first part of it.

Answer 19

yeah I know...but like I said....imagine you have 10000000000 + some small number + some other small number........

those small numbers barely make ANY difference....so you ignore then when infinity is involved

Answer 20

Okay, I get it now. Thanks so much for your help:)

Answer 21

glad you understand it :) anytime :)