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

Oct 22, 2015

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 $2 - 2 {e}^{x}$ becomes of no consequence in its effect. So you end up with the equivalent of just $- \frac{3}{2} \times \frac{{e}^{x}}{{e}^{x}} = - \frac{3}{2}$

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!!!!