SOLUTION: Identify the equation of the vertical and horizontal asymptotes of the following function: Q(x) = 4x + 7x^2 / x^2 - 7x + 12. Thanks

Algebra ->  Graphs -> SOLUTION: Identify the equation of the vertical and horizontal asymptotes of the following function: Q(x) = 4x + 7x^2 / x^2 - 7x + 12. Thanks      Log On


   

Question 320132: Identify the equation of the vertical and horizontal asymptotes of the following function: Q(x) = 4x + 7x^2 / x^2 - 7x + 12.
Thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Q%28x%29+=+%284x+%2B+7x%5E2%29+%2F+%28x%5E2-7x+%2B+12%29
Q%28x%29=%28x%284x%2B7%29%29%2F%28%28x-3%29%28x-4%29%29
There are two vertical asymptotes, when the denominator equals zero:
x-3=0
x=3
.
.
.
x-4=0
x=4
.
.
.
Q%28x%29+=+%284x+%2B+7x%5E2%29+%2F+%28x%5E2-7x+%2B+12%29

Q%28x%29+=+%284%2Fx+%2B+7%29+%2F+%281-7%2Fx+%2B+12%2Fx%5E2%29
lim%28x-%3Einfinity%2CQ%28x%29%29=%28%280%2B7%29%2F%281-0%2B0%29%29=7
The horizontal asymptote is y=7.