How do you identify all asymptotes for #f(x)=(x-1)/(x-4)#?
1 Answer
Sep 27, 2016
vertical asymptote at x = 4
horizontal asymptote at y = 1
Explanation:
The denominator of y cannot be zero as this would make y 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-4=0rArrx=4" is the asymptote"# Horizontal asymptotes occur as
#lim_(xto+-oo),ytoc" ( a constant)"# divide terms on numerator/denominator by x
#y=(x/x-1/x)/(x/x-4/x)=(1-1/x)/(1-4/x)# as
#xto+-oo,yto(1-0)/(1-0)#
#rArry=1" is the asymptote"#
graph{(x-1)/(x-4) [-10, 10, -5, 5]}