Question

What are the asymptotes of: `f(x)= (3e^(x))/(2-2e^(x))`?

Answer 1

See explanation: Only part solution given. Left some thinking for you to do!

Explanation:

Given that `x` is positive

If it gets bigger and bigger then the single left hand 2 in `2-2e^x` becomes of no consequence in its effect. So you end up with the equivalent of just `-3/2 times (e^x)/(e^x) = -3/2`

If it tends to `0^+` then `e^x` tends to 1 so we end up with
the denominator being negative and getting smaller and smaller. Consequently when divided into the denominator the result is an ever increasing negative y value but on the positive side of the x-axis.

Using the graph and the approach I have demonstrated you should be able to determine the behaviour if `x` is negative.

No you try it with `x` being negative!!!!