Question

Which function does NOT have a vertical asymptote?

A. y= (5x)/(x+x^2)
B. y=(x)/ (1-x^2)
C. y= (5x)/ (1-2x^2)
D. y= (5x-1)/ (3+x^2)

I think it is D. y= (5x-1)/ (3+x^2) not sure!

Please help and explain. Thank you!

Answer 1

You are correct because 3+x^2 = 0 has no real numbered solutions

Answer 2

so if x is a real number, then it is impossible for the denominator 3+x^2 to be 0