How to find the horizontal asymptote?

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1 Answer
Jim G.
Jan 5, 2018

#"see explanation"#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

#"solve "x=0" is the asymptote"#

#"horizontal asymptotes occur as"#

#lim_(xto+-oo),f(x)toc" (a constant)"#

#"divide terms on numerator/denominator by x"#

#f(x)=((2x)/x+1/x)/(x/x)=(2+1/x)/1=2+1/x#

as #xto+-oo,f(x)to2+0#

#rArry=2" is the asymptote"#
graph{(2x+1)/x [-10, 10, -5, 5]}

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