Finding the range of reciprocal graphs

How do I find the range of the graph

(2x-3)/(x-2)
for x > 2

thanks

you can rewrite it as (2x - 4 )/(x -2) + 1/(x - 2)

===> 2 + 1/(x - 2)

after that you should be able to figure it out by comparing with f(x) = 1/x

you can rewrite it as (2x - 4 )/(x -2) + 1/(x - 2)

===> 2 + 1/(x - 2)

after that you should be able to figure it out by comparing with f(x) = 1/x

is this the best way to do it?
is there any other way???

Original post by jsmith6131

is this the best way to do it?
is there any other way???

you could let x become v.large and notice that y tends to a certain value; i prefer my other method

you could let x become v.large and notice that y tends to a certain value; i prefer my other method

nice!
thanks

You can divide through by x to give the following

f(x) = \dfrac{2x-3}{x-2} = \dfrac{2-\frac{3}{x}}{1-\frac{2}{x}}

As x tends towards infinity 1/x tends towards 0 so that f(x) tends towards 2 so f(x)>2

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