Question

why is the line y=-x an asymptote for the graph of y=(1-x^2)/x

Answer 1

Because the line in the graph draws towards y=-x but never touches it.

Answer 2

Divide (1-x^2) by x to get


(1-x^2)/x = 1/x - (x^2)/x = 1/x - x


So we get 1/x - x


Now if x approaches infinity, then 1/x will get very very small (and will approach zero)


So when x approaches infinity, 1/x will basically go away. This leaves us with -x


So the slant (or oblique) asymptote is y = -x

Answer 3

thank you!