Thread: Confusion in sketching this graph

There appears to be an x-intercept at , but I thought there is an asymptote at the x-axis since the denominator has a greater degree than the numerator?

Whether the x-axis is an asymptote describes the behavior of the function as x approaches infinity, and whether there is an x-intercept at x = 1 describes the behavior around x = 1. Both can be true.

There is a horizontal asymptote at y= 1. There are no vertical asmptytotes because the denominator is never 0.

Isn't horizontal asymptote at y = 0?

Yes, of course. That was a typo. (That's my story and I'm sticking to it!)