SOLUTION: Identify any intercepts and asymptotes of the following: f(x)= 2x-1/x-5

Question 5747: Identify any intercepts and asymptotes of the following:
f(x)= 2x-1/x-5
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
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.
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