We have been given two functions:
[tex]y=2^x[/tex] and [tex]y=2^{-x}[/tex]
Question says that graph of [tex]y=2^x[/tex] and [tex]y=2^{-x}[/tex] are symmetric about a line. Now we have to find that line of symmetry.
So let's graph both equations to find that line of symmetry.
we can plug any number for x like -3, -2, -1, 0, 1, 2, ...
for x=2, we get [tex]y=2^x=2^2=4[/tex]
So we get point (2,4)
Same way we can find more point then graph those points and join them
We can repeat same process for other equation [tex]y=2^{-x}[/tex]
So the graph will look like the attached picture.
From graph we can see that both lines are mirror image that is symmetric about the y-axis .
Hence final answer is that line of symmetry is y-axis. or you can say x=0.
