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# What is the relationship between the graphs of y = 2^x and y = 2^-x?

Feb 8, 2016

They are mirror-images of each other, the $y$-axis being the mirror.

#### Explanation:

Both cross the $y$-axis at $\left(0 , 1\right)$ because ${2}^{0} = {2}^{-} 0 = 1$

${2}^{x}$ shows an exponential increase which doubles for every $+ 1$
${2}^{-} x$ shows an exponential decrease which halves for every $+ 1$

I will show you the graphs below (sorry I can't put them in one graph)
graph{2^x [-16.02, 16, -8.01, 8.01]}
graph{2^-x [-16.02, 16, -8.01, 8.01]}