Question #91dac

1 Answer
Somebody N.
Dec 12, 2017

See below.

Explanation:

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

Vertical asymptotes occur where the function is undefined:

For #x=1# , #y=x^2/(x-1)# is undefined, so:

The line #color(blue)(x=1)# is a vertical asymptote.

as #x-> oo# , #color(white)(88)x^2/(x-1)->oo#

as #x-> -oo# , #color(white)(88)x^2/(x-1)->-oo#

Since the degree of the numerator is greater than the degree of the denominator, there will be an oblique asymptote. We can find this by dividing the numerator by the denominator.

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

We only need to go this far with the division.

So the line #color(blue)(y=x+1)# is an oblique asymptote.

Graph:

enter image source here

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