How do you find all the asymptotes for function y=3(2)^(x-1) ?

1 Answer
Aug 3, 2018

y=3/2(xln(2)+1) for x to 0

Explanation:

In order to find eventual asymptotes, you have to find all critical points.
Also, y=e^ln(x)<=>3*2^(x-1)=e^ln(3*2^(x-1))=3e^((x-1)ln(2))=3/2e^(xln2)

y^'=(3ln2)/2e^(xln2)

Now, critical points exist if at any points, y^'=0, but e^x never decrease to 0 for any x in RR, so there is no asymptotes in +-oo for function y, however, when x to 0, you can use a limited development to find an oblic asymptote :

y=3/2(xln(2)+1)

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