Question

How do I find the horizontal asymptote for (-4x^6+6x+3)/(8x^6+9x+3)

Answer 1

leading exponents are equal.... so horizontal asymptote is ratio of leading coefficients

--> y = -4/8 = -1/2

Answer 2

welcome, congradulations on asking your first question!

Answer 3

Thank you @dumbcow! How would I find the vertical asymptote then? I'm trying to find the vertical asymptote and hole of y=(x-5)/(x^2+4x+3) as well. I just want to know how to find it, I'll find the answer myself.

Answer 4

for vertical asymptote ... set denominator equal to zero

Answer 5

a hole occurs when a factor in denominator cancels with factor in numerator
\[\frac{(x-3)(x+1)}{x-3} = x+1\]
here there is a hole at x=3 not a vertical asymptote

Answer 6

Would my vertical asymptote be equal to -5 and the hole at -3 then in y=(x-5)/(x^2+4x+3)?

Answer 7

no
\[\frac{x-5}{(x+1)(x+3)}\]
2 vertical asymptotes at x=-1 and -3

nothing cancels so a hole does not exist

Answer 8

Thanks! Last question... Would y=3/(4x-12) be stretched by 3 and translated horizontally by 12 in comparison to y=1/x?

Answer 9

Or would it be shrunk by 0.75 and translated horizontally by 0.25?

Answer 10

@dumbcow