Posted by **john** on Wednesday, December 2, 2009 at 9:59pm.

find the range of the following functions

g(x) =x/x-2

- PRE CALCULUS -
**Reiny**, Wednesday, December 2, 2009 at 10:02pm
If you mean

g(x) = x/(x-2) then the range is all real values of y except y = 1

- PRE CALCULUS -
**john**, Wednesday, December 2, 2009 at 10:05pm
how did you get that and how would you graph this function

- PRE CALCULUS -
**Reiny**, Wednesday, December 2, 2009 at 10:17pm
as x --> ±∞

the value of x/(x-2) approaches 1, but no value of x will give us 1

try solving 1 = x/(x-2)

x-2 = x

0 = 2 , which is a contradiction, so no value of x makes x.(x-2) equal to 1

e.g. let x = 1000000

then g(x) or y = 1000000/999998 = 1.000002

let x = -1000000

then y = -1000000/-1000002 = .999998

so y = 1 is a horizontal asymptote

there is also a vertical asymptote at x=2, since x=2 makes y undefined.

the graph will be a hyperbola with major axis as y = x - 1 and centre (2,1)

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