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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.
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