Question

Please Help me. I don't understand it.

1. Identify the vertical asymptotes of
f(x) = 2/x^2+3x-10

2. Identify the vertical asymptotes of f(x) = x+6/x^2-9x +18

3. Identify the horizontal asymptote of f(x) =4x/7

4. Identify the horizontal asymptote of f(x) = 7x+1/2x-9

5.Identify the horizontal asymptote of f(x) = x^2+5x-3/4x-1

6. Identify the oblique asymptote of f(x) = x^2-4x+8 /x+2

7.Identify the oblique asymptote of f(x) = 2x^2+3x+8/x+3

8.Identify the oblique asymptote of f(x) = x+4/3x^2+5x-2

9. Identify the oblique asymptote of
f(x) =4x^2-x+2/x+1

Answer 1

A few pointers:
VA: Look for points where the function is not defined.
HA: We have cases:
Case 1: deg(numerator)>deg(denom) -> no HA
Case 2: deg(num)=deg(denom) -> HA is given by y=m/n where m and n are the coefficients of the highest powers in the numerator and the denominator.
Case 3: deg(num)<deg(denom) -> y=0 is the HA
OA: Divide the numerator by the denominator using long division. The OA is y={the remainder}.

Answer 2

How do i find where the function is not defined?

Answer 3

When it gives you 1/0 , it is undefined

Answer 4

Okay. Now will you please work out one of the problems of each so i can see how it looks.

Answer 5

Oops. In the OA, I meant y={the quotient}, not the remainder. :))

Answer 6

Now, i'm just confused again. When it gives me 1/0 it is undefined. How do i work the problem to find if it's undefined?

Answer 7

Look at where the denominator is 0. In 1, for example, x^2+3x-10=0 iff (x+5)(x-2)=0 and this means that vertical asymptotes for this function are x=-5 and x=2.

Answer 8

In 4, we see that the degree of the numerator is equal to the degree of the denominator. Thus, the HA is y=7/2.

Answer 9

Lastly, in 9, if you perform the long division, you get 4x-5 with some remainder. Therefore, y=4x-5 is the oblique asymptote.

Answer 10

So for #2 it would be X=6 x=3... Is it Correct

Answer 11

If it's wrong tell me don't give me the answer i'll try again. Okay.

Answer 12

But it is correct o.o

Answer 13

Okay :) . For #5 Is it y=1/6

Answer 14

I'm not sure for (5), I though it had an oblique asymptote instead of a horizontal one. Sorry that I can't help :(

Answer 15

Oh. Okay what about #7 y = 2x – 3

Answer 16

Yes, it should be

Answer 17

Thank you. for #8 : I'm entirely sure. Is it y = 3x + 17

Answer 18

Is the question
\[ f(x) =\frac{ x+4}{3x^2+5x-2}\]

Answer 19

Yes it is.

Answer 20

I think it should have no oblique asymptotes but it has vertical asymptotes. If the highest power of the unknown is the numerator is smaller than that of denominator, it has no oblique asymptotes, I think.. (in this case, 1 in numerator is smaller than 2 in denominator) That's what I've learnt

Answer 21

Okay . Thank You once again.

Answer 22

Welcome :)

Answer 23

What is #6