extrema, intercepts, symmetry, asymptotes

[abby_07]

please help me with this problem
i need to find the extrema, intercepts,symmetry, asymptotes of
y=x-3/x-2

to find the extrema i found the derivative of y
y'=1(x-2)-(x-3)(1)/(x-2)^2
y'=1/(x-2)^2=0
thus i found that there are no critical points so there is no extrema ( i dont know if this is right)

after graphing y i think the asyptotes is at x=2

and the intercepts is at (3,0)
although i do not no about the symmetry
can you help please

 

[stapel]

y=x-3/x-2

Does the above actually mean "y = (x - 3) / (x - 2)", also written as follows:

. . . . .\(\displaystyle \L y\, =\, \frac{x\, -\, 3}{x\, -\, 2}\)

Or did you mean "y = x - (3/x) - 2", as you posted? (The answer to the exercise depends on what the original function was, is why I ask.)

Thank you.

Eliz.

 

[abby_07]

sorry about that the problem is
y = (x - 3) / (x - 2)