How do I tell if this is a vertical/horizontal/oblique asymptote?

[38175425]

2x^2 / x^2 = 2/1 = 2
But how do I tell if this is a vertical/horizontal/oblique asymptote?

 

[skeeter]

oblique linear asymptotes occur when the degree of the numerator is one greater than the degree of the denominator, and both have no common linear factors

vertical asymptotes occur where the denominator equals zero and has no common factor with the numerator

[imath]y= \dfrac{2x^2}{x^2}[/imath] has a removable discontinuity (a hole) at x = 0

 

[Steven G]

What you wrote in incomplete.

You should have written y=2x^2 / x^2 = 2/1 = 2 when x is large.

Oh, y=2 when x is large. y=2 is a horizontal line. Hence y=2 is the horizontal asymptote.

 

[pka]

2x^2 / x^2 = 2/1 = 2
But how do I tell if this is a vertical/horizontal/oblique asymptote?
View attachment 34661

How? If I were I would simply look ar a plot of that function: SEE HERE
Scroll down to the second plot.

 

[38175425]

thank you!