Question

For the function y=4x^2+5/x^2-6x+9, do both of the following:
a. State the vertical asymptote of the function and describe how you found it
b. State the horizontal asymptote of the function and describe how you found it

Answer 1

I will assume you meant:
y= (4x^2+5)/(x^2-6x+9)
y = (4x^2 + 5)/(x-3)^2

The denominator is zero when x = 3, so we have a vertical asymptote at x = 3

y= (4x^2+5)/(x^2-6x+9)
y= (4 +5/x^2)/(1 - 6/x + 9/x^2) , I divided top and bottom by x^2

Limit (4 +5/x^2)/(1 - 6/x + 9/x^2) as x ----> ± ∞
= 4

so we have a horizontal asymptote at y = 4

https://www.wolframalpha.com/input/?i=graph+y%3D+%284x%5E2%2B5%29%2F%28x%5E2-6x%2B9%29+from+-20+to+20

Answer 2

thank you for the help, although I wrote the problem exactly from what was on the assignment

Answer 3

When you write fractions on line, you must place brackets in the proper places to assure
the order of operation is maintained.
e.g. Just typing y=4x^2+5/x^2-6x+9 , would result in 5 ÷ x^2 as the only division
e.g. Here is how Wolfram would see it
https://www.wolframalpha.com/input/?i=y%3D4x%5E2%2B5%2Fx%5E2-6x%2B9