Symmetric graphs

[Fernando Revilla]

I quote a question from Yahoo! Answers

f(x)=3^x and g(x)=(1/3)^x I put that they mirror each other, that they are symmetrical. I am obviously missing something important between the two

I have given a link to the topic there so the OP can see my response.

 

[Fernando Revilla]

Denote $f(x)=3^x$ and $g(x)=(1/3)^x=1/3^x=3^{-x}$ and $\Gamma (f)$, $\Gamma (g)$ their respective graphs. Then, $$(x,y)\in\Gamma (f)\Leftrightarrow y=3^x \Leftrightarrow y=3^{-(-x)}\Leftrightarrow (-x,y)\in \Gamma (g)$$ This means that $f$ and $g$ are symmetrical with respect to the $y$-axis.