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