How do you graph #y= (2x)/(x-1)#?

1 Answer
Alan P.
Jul 31, 2015

Graph as #y = (2x)/(x-4)#
by establishing a few data points with random values of #x# and noting the asymptotic limits at #y=2# and #x=1#

Explanation:

The asymptotic limit #x=1# should be obvious from the expression (since division by 0 is undefined).

#y=(2x)/(x-1)# is equivalent to #y=2/(1-1/x)# [provided we ignore the special case #x=0#]
As #x rarr +-oo#
#color(white)("XXXX")##1/x rarr 0#
and
#color(white)("XXXX")##y=2/(1-1/x) rarr 2/1 = 2#
giving the horizontal asymptotic limit.

A few test values for #x#, such as
#color(white)("XXXX")##x=-1 rarr y = -1#
#color(white)("XXXX")##x=0 rarr y=0#
#color(white)("XXXX")##x=2 rarr y = 4#
#color(white)("XXXX")##x=3 rarr y= 3#

help give shape to the graph

graph{(2x)/(x-1) [-25.3, 26, -11.27, 14.4]}

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