Question 5747
First, know the general shape of this type of equation. This helps you.


ASYMPTOTES:
when x=5, denominator is zero --> asymptote 1.

Re-arrange the equation to give x = equation in y. This denominator then will show that y cannot be 2... second asymptote.


When x = 0, y=?


When y = 0, x=? (just less than 2


When x is HUGELY +ve, what happens to (2x-1)/(x-5)? well, we can ignore the -1 and -5 --> 2x/x so it tends towards +2.
When x is HUGELY -ve, what happens to (2x-1)/(x-5)? well, we can ignore the -1 and -5 --> -2x/-x so it tends towards +2 again.


--> these 2 confirm the asymptotes.


Sketch the graph now.


jon.