How do you find any asymptotes of #f(x)=x/(x-5)#?

2 Answers
May 16, 2018

Answer:

VA: #x = 5#
HA: #y=1#

Explanation:

(VA) Vertical Asymptote: Set the denominator equal to zero:

#x-5 = 0#

#x = 5#

(HA) Horizontal Asymptote: Divide the coefficients of the x values:

#(1x)/(1x)=1#

#y=1#

May 16, 2018

Answer:

#"vertical asymptote at "x=5#
#"horizontal asymptote at "y=1#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero 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-5=0rArrx=5" is the asymptote"#

#"horizontal asymptotes occur as"#

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

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

#f(x)=(x/x)/(x/x-5/x)=1/(1-5/x)#

#"as "xto+-oo,f(x)to1/(1-0)#

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