Question

find the vertical asymptotes, if any, of the graph of the following rational function. f(x)=x/x^2+8... i do not understand this. please explain how to solve this

Answer 1

I'm assuming the denominator is x^2 + 8 correct?

Answer 2

or is it just x^2 ?

Answer 3

assuming x^2+8 is the denominator, this would mean that if x^2 + 8 was zero, then


x^2 + 8 = 0

x^2 = -8

x = sqrt(-8)

since taking the square root of a negative number gives you a complex/imaginary number, this means that there are no real solutions to x^2 + 8 = 0

Answer 4

what this means is that x/(x^2 + 8) will have no real values of x which make the denominator zero

so you don't have to worry about division by zero errors and that means there are no vertical asymptotes

Answer 5

thank you so much! lol ten more ?s to go! god this stuff confuses me lol

Answer 6

you're welcome