Question

Find the horizontal or oblique asymptote of f(x) = negative 3 x squared plus 7 x plus 1, all over x minus 2. WILL GIVE MEDAL JUST PLEASE HELP

Answer 1

@Destinymasha please help

Answer 2

@pooja195

Answer 3

If there's a restriction to the function, then there's an asymptote presented. One way we know if there's a restriction is to see if there's a restriction to the denominator, like what makes it equal to zero. In this case, if we set the denominator equal to zero and found the restriction value, then that value is the vertical asymptote.

Answer 4

2?

Answer 5

Finding the horizontal asymptote is different. If there's a lower degree on the denominator than in the numerator, then horizontal asymptote doesn't exist. But if the degrees are the same, you'd just divide by the first term of the numerator and the first term of the denominator which in this case, you don't have in your polynomial.

Answer 6

If the degree is higher in the numerator, then there could be a slant asymptote instead.

Answer 7

So what does that mean as far as answering the problem? my options are :
y=2
y=-3
y=3x+7
y=-3x+1

Answer 8

@snugglemuffinman i'm not telling you the answer directly, i'm showing you how to get the answer. So please, follow along.

Answer 9

There's no horizontal asymptote so we proceed to find the slant asymptote instead. Do you have any ideas of how to find slant asymptotes?

Answer 10

No, the only asymtopes I learnt about are vertical, horizontal, and oblique.

Answer 11

Oblique and slant asymptotes are the same.

Answer 12

Do you have any ideas of how to find oblique asymptotes? Is this your first problem to work with asymptotes?

Answer 13

I learned about it many many weeks ago and totally forgot how to do it.

Answer 14

To find oblique asymptotes, you must factor the numerator and the denominator (if they can be factored further). Once you're done factoring and breaking down, you'll get a polynomial that is not in fractions and usually broken down to a line equation (y=mx+b), That polynomial will be your oblique asymptotes.

Answer 15

So, simply factor the numerator. Can you do that?

Answer 16

I don't think it does factor out since none of the factors of 3 whose sum equals the coefficient of the middle term are 7 .

Answer 17

Consider synthetic or long division instead. If fractions can't be factored then divide them instead. For oblique asymptotes, we want to break down the numerators as possible.

Answer 18

I don't know how to do that....

Answer 19

i'll show you how. Let me first fix my drawing tool by refreshing the page >.<

Answer 20

Just like any long division with numbers, we are trying to find what quotient that when multiplied by the divisor, we get the dividend as the result.