Good morning! Please help:

Give the equation of the horizontal asymptote, if any, of the function h(x)=8x-6/x-2

Thanks, you will get a medal for the best answer! :)

Question

Good morning! Please help:

Give the equation of the horizontal asymptote, if any, of the function h(x)=8x-6/x-2

Thanks, you will get a medal for the best answer! :)

rock_mit182 · Answer

2(4x-3)/x-2 i believe the horizontal asymptote is when the numerator becomes zero

anonymous · Answer

it's multiple choice, a)y=0 b)y=8 c)y=2 d)no h.a.

rock_mit182 · Answer

the graph looks like this|dw:1397315609675:dw|

ipwnbunnies · Answer

Horizontal asymptote rule:
When the numerator and denominator have the same degree polynomial, divide the coefficients of the monomials with the highest degree.

rock_mit182 · Answer

oh now i remembered how to find the vertical asymptote you have to divide by x numerator and denominator as well

ipwnbunnies · Answer

Not necessarily. You set the denominator equal to 0, solve for x. That'll be the equation of the vertical asymptote.

anonymous · Answer

so the answer would be y=0?

ipwnbunnies · Answer

No, try again. What's the highest degree monomial of the numerator and denominator?

anonymous · Answer

y=8

rock_mit182 · Answer

no! look at the graph where the horizontal  asymptote cuts the y- intercept

rock_mit182 · Answer

;)

anonymous · Answer

2

ipwnbunnies · Answer

Oh, now I understand your graph lol.
How did you get y=8? Did you look at his graph?

anonymous · Answer

yes IPwn Bunnies, maybe I looked incorrectly....pardon, still learning precalc

ipwnbunnies · Answer

If you think about it, the horizontal asymptote would be equal to the limit of the equation as x approaches infinity.

ipwnbunnies · Answer

Oh, precalc. Forget the limit stuff lol.

anonymous · Answer

0 since 8 and 2 are wrong! :)

ipwnbunnies · Answer

I didn't say they were wrong. What's the degree of the polynomial in both of the numerator and denominator?

rock_mit182 · Answer

no they are not wrong a think limits is too advanced for you you need a pre.calculus aproach

ipwnbunnies · Answer

That means the variable has the highest power of what?

anonymous · Answer

x to the first power

anonymous · Answer

8x-6 divided by x-2

ipwnbunnies · Answer

Good, that is in both the numerator and the denominator. According to the horizontal asymptote rules, the horizontal asymptote occurs at y-value of when you divide the coefficients of both x terms.

anonymous · Answer

I see

ipwnbunnies · Answer

So, what's the coefficient of the x term in the numerator? The denominator? Then, divide them. That's be your horizontal asymptote, y=?

anonymous · Answer

coeff is 8 in the numerator and 1 in the denominator

ipwnbunnies · Answer

There ya go. 8/1 = 8. So the horizontal asymptote occurs at y = 8.

Note, this rule only applies to when the numerator and denominator have the same degree polynomial.

anonymous · Answer

8x divided into 1x equals 8

anonymous · Answer

Thanks iPwnBunnies, got any suggestions on other references to learn precalc because I have calculus next semester in the Fall

ipwnbunnies · Answer

I don't have other references lol. Just study hard. Precalc sorta prepares you for calculus, but not much.

anonymous · Answer

I will keep in touch with you, you got the medal and a testimony from me!

ipwnbunnies · Answer

Thank you man. Good luck. :)