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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