Question

find the HORIZONTAL asymptote, if any, of the graph of the rational function

f(x)= 25x/5x^2+1

A) y = 5
B) y = 1/5
C) y = 0
D) no horizontal asymptote?

Answer 1

For horizontal asymptotes, the degree of polynomial of the numerator of the fraction should be the same as the degree of polynomial of the denominator of the fraction.
Can you work out the answer now?

Answer 2

so it should be no horizontal asymptote cause 5x^2+1 = 0
5x^2 = -1?

Answer 3

or 25 (x)/ 5 (x^2 +1) = 5 (x) / (x^2 +1) right there?

Answer 4

No. If you're doing in that way, you're trying to find the VERTICAL asymptotes.
To find horizontal asymptotes, you actually need to take limit. But for this question, it's quite obvious because my little trick works. :S

Answer 5

I know how to get the vertical what about the horizantal? is this correct?

25(x)/ 5(x^2+1) = 5x/x2+1?

Answer 6

No, it is not. 5 is not the common factor for denominator. You cannot do it like that.

Answer 7

is it 5?

Answer 8

No.

Answer 9

Take limit for the function, x tends to infinity, to find the horizontal asymptotes, or arrange the function in the form \(f(x) = C + \frac{P(x)}{Q(x)}\). Horizontal asymptotes is at y = c.

Answer 10

*Horizontal asymptotes is y = c.

Answer 11

I still didn't understand it

Answer 12

I still don't get it.

Answer 13

Have you learnt limit?

Answer 14

Nope

Answer 15

Alright. Then use the second method..
Example:
\(f(x)= \frac{5x^2+3}{5x^2+1}\)
It can be rearranged in the form C + P(x)/Q(x)
\[f(x)= \frac{5x^2+3}{5x^2+1}\]\[=\frac{5x^2+1+2}{5x^2+1}\]\[=\frac{5x^2+1}{5x^2+1}+\frac{2}{5x^2+1}\]\[=1+\frac{2}{5x^2+1}\]
So, the horizontal asymptotes is y=1.
Got it?

Answer 16

I'm gonna take note of that GOT IT SIR

Answer 17

Miss, not sir :)

Answer 18

Wait don't go yet I want to make sure my answer is correct

Answer 19

I'll leave in 5 minutes.. I'm sorry!

Answer 20

so this is it. I followed what you did. 5x(5) / 5x (x+1) is that correct?

Answer 21

Nope :|

Answer 22

Oh. I'm dumb flutter

Answer 23

Calm...
Observe the denominator and the numerator.. and compare..

Answer 24

they have both x. and multiples of 5

Answer 25

No. of terms?

Answer 26

Sorry, have to go now...

Answer 27

alright thanks for your help though.