SOLUTION: Hi, I have to find the vertical/horizontal asymptotes as well as the y-intercept of the following: {{{y=(x-1)/(2x^2+5x-3)}}} Vertical Asymptotes: {{{-2x + 1 = 0}}} {{{-x-3=

Algebra ->  Equations -> SOLUTION: Hi, I have to find the vertical/horizontal asymptotes as well as the y-intercept of the following: {{{y=(x-1)/(2x^2+5x-3)}}} Vertical Asymptotes: {{{-2x + 1 = 0}}} {{{-x-3=      Log On


   

Question 369295: Hi, I have to find the vertical/horizontal asymptotes as well as the y-intercept of the following:
y=%28x-1%29%2F%282x%5E2%2B5x-3%29
Vertical Asymptotes:
-2x+%2B+1+=+0
-x-3=0
x = 1%2F2
x = -3
Horizontal Asymptote:
x-1=0
x = 1
y-intercept:
%28-1%29%2F%28-3%29
y = 1%2F3
I think I've got it, but I just want to check. I've been struggling with these. Thanks so much :)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
You're a little mixed up about how to find horizontal asymptotes.
You don't set the numerator equal to 0 to find the horizontal
asymptote.  Apparently that's what you were thinking.  You need to
review how to find horizontal asymptotes.

y=%28x-1%29%2F%282x%5E2%2B5x-3%29

You found vertical asymptotes OK:

Set denominator = 0

2x%5E2%2B5x-3+=+0
Factor:
%282x-1%29%28x%2B3%29=0

2x-1=0
2x=1
x=1%2F2  That's the equation of one vertical asymptote

x%2B3=0
x=-3  That's the equation of the other asymptote

Here they are:

 

Since the largest exponent in the top is smaller than the exponent in the
bottom, the x-axis, whose equation is y=0, is the horizontal asymptote:

 

It's hard to tell what the graph does on the right. It crosses the
x-axis at 1, it goes up just a tiny bit (less than one tenth),
then it goes back down and approaches the x-axis on the right.

Edwin