F(x)=(2x-1)/ (|x| -3)

Question

Rewrite f(x) as a piecewise function. Then find the limit as it approaches positive infinity and negative infinity.

Answer 1

for x<0, |x| = -x. So, we have

f(x) =
(2x-1)/(-x-3) for x<0
(2x-1)/(x-3) for x>=0.

Now you can easily find the limits, no?

To confirm your answer, see

http://www.wolframalpha.com/input/?i=%282x-1%29%2F+%28|x|+-3%29

and scroll down to where it describes the limits.