some direction please

[thegersters]

Which of the lines below is a slant (or oblique) asymptote for the graph of
y = (x2 - x - 1)/(x - 1).


Can someone give me some direction?

 

[soroban]

Hello, thegersters!

Which of the lines below is a slant (or oblique) asymptote for the graph of
y = (x² - x - 1)/(x - 1)
.

To find a slant asymptote, take limit of y as x -> infinity.

. . . . . . . . . . . . . . . . . . . . . . x² - x - 1 . . . . . . . 1
Using long division: . y . = . ----------- . = . x - ------
. . . . . . . . . . . . . . . . . . . . . . . .x - 1 . . . . . . . . x - 1

. . As x gets larger and larger, that fraction goes to 0.

Hence, the graph approaches the line: .y = x