Asked by jasmineT

f(x)=[5x^3-4x^2-8x+9]/[2x^2-1x-3]

Find the equation of the non-vertical asymptote.
y =

Does f(x) intersect its non-vertical asymptote? (yes or no)

What is the smallest value of x at which f(x) intersects its non-vertical 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 :)
Answered by Reiny
your y = 2.5x - .75 is correct, (obtained by division)

so now we have to intersect
y = [5x^3-4x^2-8x+9]/[2x^2-1x-3] and y = 2.5x - .75

[5x^3-4x^2-8x+9] = [2x^2-1x-3][2.5x - .75]
[5x^3-4x^2-8x+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 non-vertical asymptote at x = 5.4

Wolfram seems to agree with me
http://www.wolframalpha.com/input/?i=%5B5x%5E3-4x%5E2-8x%2B9%5D%2F%5B2x%5E2-1x-3%5D+%3D+2.5x+-+.75
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