Posted by jasmineT on Monday, March 12, 2012 at 12:26am.
f(x)=[5x^34x^28x+9]/[2x^21x3]
Find the equation of the nonvertical asymptote.
y =
Does f(x) intersect its nonvertical asymptote? (yes or no)
What is the smallest value of x at which f(x) intersects its nonvertical asymptote? ( Enter No in the question blank if you answered no above.)
I got the answer to the first two parts, y=2.5x.75 and yes. But i don't know how to figure out the last part of the question. Please help :)

calc  Reiny, Monday, March 12, 2012 at 8:24am
your y = 2.5x  .75 is correct, (obtained by division)
so now we have to intersect
y = [5x^34x^28x+9]/[2x^21x3] and y = 2.5x  .75
[5x^34x^28x+9] = [2x^21x3][2.5x  .75]
[5x^34x^28x+9] = 5x^3  1.5x^2  2.5x^2 + .75x  7.5x + 2.25
1.25x = 6.75
x = 5.4
yes, f(x) intersects its nonvertical asymptote at x = 5.4
Wolfram seems to agree with me
http://www.wolframalpha.com/input/?i=%5B5x%5E34x%5E28x%2B9%5D%2F%5B2x%5E21x3%5D+%3D+2.5x++.75