What are the asymptotes and removable discontinuities, if any, of #f(x)=(x-12)/(2x-3) #?
1 Answer
Jun 10, 2016
vertical asymptote
horizontal asymptote
Explanation:
Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation set the denominator equal to zero.
solve : 2x - 3 = 0
#rArrx=3/2" is the asymptote"# Horizontal asymptotes occur as
#lim_(xto+-oo),f(x)toc" (a constant)"# divide terms on numerator/denominator by x
#(x/x-12/x)/((2x)/x-3/x)=(1-12/x)/(2-3/x)# as
#xto+-oo,f(x)to(1-0)/(2-0)#
#rArry=1/2" is the asymptote"# There are no removable discontinuities.
graph{(x-12)/(2x-3) [-10, 10, -5, 5]}