find vertical asymptote of function (image attached. I don't understand why the vertical asymptote is -1/2, as the e^2x and e^x do not have the same powers?

Question

anonymous · Answer

attachment

sdfgsdfgs · Answer

vertical asymptote means at a certain x value(s), f(x) will become infinity/undefined. look at the example shown here for vertical asymptote: http://mathworld.wolfram.com/Asymptote.html

sdfgsdfgs · Answer

looking at the expression for f(x) n keep in mind anything divided by 0 will be infinity...

sirm3d · Answer

the graph of a function has a vertical asymptote whenever the denominator becomes zero at some value while the numerator does not evaluate to zero at that value.

anonymous · Answer

it is not -1/2. if u set e^x-2=0 then u get e^x=2, apply "Ln" on both sides... then what do u get?

anonymous · Answer

there are 2 asymptotes: ln2 and -1/2. I'm just confused as to how the -1/2 was calculated.. was limits used? @mlearning24 @sirm3d @sdfgsdfgs

thomas5267 · Answer

-1/2 is not a vertical asymptote of the function.

anonymous · Answer

@thomas5267 -1/2 is the horizontal asymptote.

anonymous · Answer

You can find horizontal asymptotes by checking the end behavior of the function.

What are the values of the limits,
$$\lim_{x\to\pm\infty}f(x)~?$$

sdfgsdfgs · Answer

the horizontal asymptote should be y=0; according to Wolfram: https://www.wolframalpha.com/input/?i=y%3D%28e%5E%282x%29+%2B1%29%2F%28e%5Ex-2%29