# on which intervals f(x) is increasing...

• Mar 28th 2013, 05:42 AM
dokrbb
on which intervals f(x) is increasing...
I have such a function f(x) = (x-4)/(x+8), and I need to find the interval on which it is increasing:

I found the derivative f'(x) = [(x+8)-(x-4)]/(x+8)^2 = 12/(x^2 + 16x + 64), and for the denumerator the only critical point is -8, and the function is positive

on the both sides of (-8),

do I have to mention the f(x) is increasing on (-Inf, -8)U(-8, Inf) ?
• Mar 28th 2013, 06:20 AM
HallsofIvy
Re: on which intervals f(x) is increasing...
Well, yes, that is the answer so you had better mention it! You could say "f is increasing for all x for which it is defined" but since you said "find the interval(s) on which it is increasing" you should specifically state the intervals. I added the "s" because it is NOT increasing on a single interval.
• Mar 28th 2013, 06:27 AM
FrancisLauTutor
Re: on which intervals f(x) is increasing...
Hi dokrbb,

Yes you are right.
increasing on (-Inf, -8)U(-8, Inf)
:)

Francis
Tutorat A+ Tutoring | Go for A+ , A big step toward the future.
• Mar 28th 2013, 06:28 AM
MINOANMAN
Re: on which intervals f(x) is increasing...
The function increases for all real x,however there is a discontinuity at the point x=-8 where the function jumps from +infinity to - infinity.. the line x=8 is a vertical asymptote and the line y=1 is a horizontal asymptote. the graph of the function itself is a hyperbola with the lines x=-8 and y=1 as its asymptotes.
• Mar 28th 2013, 06:47 AM
dokrbb
Re: on which intervals f(x) is increasing...
Quote:

Originally Posted by MINOANMAN
The function increases for all real x,however there is a discontinuity at the point x=-8 where the function jumps from +infinity to - infinity.. the line x=8 is a vertical asymptote and the line y=1 is a horizontal asymptote. the graph of the function itself is a hyperbola with the lines x=-8 and y=1 as its asymptotes.

Thanks to all of you, but can you, please, show me how did you figure out the horizontal asymptote? thanks
• Mar 28th 2013, 06:48 AM
FrancisLauTutor
Re: on which intervals f(x) is increasing...
You need to check 2 limits
You need to use limit while x approaching +inf
and limit while x approaching -inf
• Mar 28th 2013, 06:52 AM
MINOANMAN
Re: on which intervals f(x) is increasing...
get the limf(x) as x goes to infinity ..this limit =1 this is the horizontal asymptote....

get the lim f(x) as x goes to -8 (+) or to -8 (-) ( the + and - signs shows the path of the x as it goes to -8 from right or left....) anyway the line -8 is the vertical asymptote....

MINOAS
• Mar 28th 2013, 06:57 AM
dokrbb
Re: on which intervals f(x) is increasing...
Great, Thanks