What is the horizontal asymptote of 5 divided by x minus 6?

Answer 1

-1

Answer 2

As x becomes large x-6 becomes large too and 5/(x-6) becomes increasingly small in magnitude but positive. So in the +ive direction the horizontal asymptote is the x-axis.

Similarly as x becomes small x-6 becomes small and 5/(x-6) becomes increasingly small in magnitude but negative. So in the -ive direction the horizontal asymptote is the x-axis.

Tip: To see the behaviours of functions such as this easily I suggest using GeoGebra, which is free.