Question

find the horizontal asymptote of the graph y= -4x^6+6x+3/8x^6+9x+3

Answer 1

when the degree of the numerator's expression is the same degree as the degree of the denominator's expression

the horizontal asymptote is found at \(\bf y=\cfrac{\textit{leading term coefficient atop}}{\textit{leading term coefficient at bottom}}\)

Answer 2

well I know you have to factor out the top and bottom and that the answer is either y=1, y=0, y=-1/2, or there is no horizontal asymptote

Answer 3

\(\bf y=\cfrac{{\color{blue}{ -4}}x^{\color{red}{ 6}}+6x+3}{{\color{blue}{ 8}}x^{\color{red}{ 6}}+9x+3}
\)

Answer 4

Apologies. I misread the question and responded incorrectly. (Face very red.)

Answer 5

haha it's fine. It's just math isn't my strong suit and I have no idea what i'm doing.

Answer 6

Hi, Blondie,

Actually, I'd say you don't have to factor numerator and denominator. That's great for finding vertical asymptotes and zeros of the given rational expression. However, you're looking for the horiz asy. and that requires a completely different approach. Have you done a problem like this one befoer?

Answer 7

mathmale well you know you can always use "Just for Men, in Just 5 mins" =)

Answer 8

ya but I forget very easily

Answer 9

Hint: JDoe has some red-hot, right-on advice for you. Can you work with his suggestion to find the equation of the horiz. asy.? You going to treat me to a free box of JustForMen? That'd do my white hair a lot of good. Thanks for the thought!

Answer 10

hehe

Answer 11

Please note that horiz. asy. involve limits as x approaches plus or minus infinity.

Thus, as JDoe has hinted, we can ignore all terms in the rational expression except for the highest powered terms in numerator and denom.

Would you please go back to his colorful suggestion and type out the result, y = ?, if we ignore all but the x^6 terms?

Answer 12

but how do you factor out the top and bottom?

Answer 13

factor out? all you need is the leading term coefficient

Answer 14

Actually, Blondie, you don't have to do that at all IF your goal is to find the horiz. asy. I'll lead you thru both parts of this problem: finding the horiz asy and finding the vertical asy and the horiz. intercepts. Note: JDoe's advice is again right on target. Smart guy there.

Answer 15

\(\bf y=\cfrac{{\color{blue}{ -4}}x^{\color{red}{ 6}}+6x+3}{{\color{blue}{ 8}}x^{\color{red}{ 6}}+9x+3}\)

Answer 16

So, As JDoe has suggested, look at his expression and ignore EVERYTHING on the right except for what's in blue and red (but keep the x's in those terms).

Write this out, please.

Answer 17

My name on here says it all. I'm still confused. Ok I will try that^

Answer 18

Blondes are JUST AS SMART as everyone else, and YOU are NO exception!

Answer 19

I looked at the red and blue but what do I do with it?

Answer 20

Write " y = ------- " and then write JDoe's -4x^6 in the numerator and his 8x^6 in the denom.

Answer 21

ok now what?

Answer 22

As in:\[y = \frac{ -4x ^{6} }{ 8x ^{6} }\]
take a good look at that and tell me what YOU think we could do to simplify that expression.

Answer 23

-2x^6?

Answer 24

wouldn't the following\[y=\frac{ -4g }{ 8g }\] equal -4/8 ??

Answer 25

And couldn't -4/8 be reduced further?

Answer 26

and that would be -1/2 wich is one of the answers

Answer 27

Yes!!! So, Blondie, your horiz asy is simply y=-1/2. Must write that with a " y ".

Answer 28

thank you so much!(:

Answer 29

Now, want to think about the vertical asymptotes, or have I asymptoted you out already?

Answer 30

:)

Many thanks, @jdoe0001 , for your input! and also for your suggesting Just For Men. :)