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Symmetric graphs

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
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

Well-known member
MHB Math Helper
Jan 29, 2012
661
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.