Find the domain of the function and identify any horizontal and vertical asymptotes.
f(x)= 1-5x/1+2x

Question

anonymous · Answer

(1-5x)/(1+2x) would be a domain which is defined for all numbers in the domain such that x != -1/2

anonymous · Answer

vertical when x = -1/2
horizontal would be when y = -5/2

anonymous · Answer

Horizontal asymptotes if my memory serves me right are when the numerator is 0, and the vertical asymptotes are when the denominator is 0. With this said, the horizontal asymptote would be at x=1/5 and the vertical asymptote would be at x=-1/2. Someone please correct me if I am wrong. Thanks, Sean Walsh Facebook: Tutor Sean http://www.tutorsean.net

anonymous · Answer

what about for this problem f(x)= 2x2/x+1 and what about the domain for both problems

anonymous · Answer

The domain refers to the x values. And since you cannot divide by 0 you need to check and see when the denominator will be 0. so $$1 + 2x = 0$$ Solve for x $$x = -\frac{1}{2}$$ The domain is $$(-\infty,-\frac{1}{2})\cup(-\frac{1}{2},\infty)$$ And by setting the denominator equal to zero, you have also found a vertical asymptote at $$x = -\frac{1}{2}$$ Horizontal asymptotes can be found by looking at the degree of the first term in the numerator and the denominator. If they are the same then keep the leading coefficients and that is your asymptote. So in this case both of the degrees are 1 and the leading coefficients are 1/1.. Therefore you have a horizontal asypmtote at $$y = 1$$

anonymous · Answer

Domain for first is  for all real x not equal to -1/2.
and I think you typed your second equation incorrectly.

anonymous · Answer

Sean your horizontal asymptote is incorrect and Tyler you too.
You look at the coefficient of x which is the number in front of x, not the constants.

anonymous · Answer

oops.. My horizontal asymptote is incorrect.. Sorry.. it should be y = -5/2. Thanks

anonymous · Answer

You are right Stleaveland. Like I said been a long time on this one. Taking all kinds of advanced math makes for a weak algebra brain. I found this site which has a good description of how to find asymptotes. http://www.purplemath.com/modules/asymtote4.htm Hope this helps.