SOLUTION: Can someone help me solve this problem asap? 1. Find the horizonal and vertical asymptotes of the following. Type "none" if the function does not have an asymptote. A.f(x)=2x-3/x

Algebra ->  Graphs -> SOLUTION: Can someone help me solve this problem asap? 1. Find the horizonal and vertical asymptotes of the following. Type "none" if the function does not have an asymptote. A.f(x)=2x-3/x      Log On


   



Question 115406: Can someone help me solve this problem asap?
1. Find the horizonal and vertical asymptotes of the following. Type "none" if the function does not have an asymptote.
A.f(x)=2x-3/x^2+2
answer____________
Horizonal________
Vertical:____________
B. g(x)= 5x/x-1
Answer__________
Horizonal:________
Vertical_______
Thank you dearly

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
By definition, asymptote+ is a straight line continually approaching but never meeting a curve, or a line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.
1.
f%28x%29=%282x-3%29%2F%28x%5E2%2B2%29
The vertical asymptotes come from the zeroes of the denominator, so we need to set the denominator equal to zero and solve.
x%5E2%2B2=0
x%5E2+=+-2
x+=+-+sqrt%28-2%29
This has no+solution. Since the denominator has no zeroes, then+there+are+no+vertical+asymptotes and the domain is "all x".
Since the degree is greater in the denominator than in the numerator, the+y-values will be dragged down to the+x-axis, and the+horizontal+asymptote is therefore "y+=+0". Since I have found a horizontal asymptote, I don't have to look for a slant asymptote. Then the full answer is:
domain: all x+
vertical asymptotes: none+
horizontal asymptote: y+=+0 (the x-axis)
slant asymptote: none

2.
g%28x%29=+5x%2F%28x-1%29+
The vertical+asymptote is at +x+=+1.
set the denominator and set it equal to 0 :
x-1=0
=> x+=+1
a+horizontal+asymptote for this is...
lim+x--> infinity...+5x%2F%28x-1%29 -->+5
lim+x-->-infinity...+5x%2F%28x-1%29+ -->+5