Answer
All functions pass through the point (0,1). A function is the reflection around the y axis of another function when the bases are inverse numbers and the exponents are equal.
Work Step by Step
Well, first we have to plot the graphics. If you're graphing by hand, you can substitute x for a few values in each case, to get an idea of how fast the function will grow, and then just plot, remembering the 'shape' of the exponential functions. In our case, we have the image below:
Then we want to know how the graphics are related. We can see that they all intersect at the point (0.1), right?
Because whenever x=0, we have a number raised to zero, which is 1. Every exponential function, regardless of the base, will go through this point. We also see that the functions y=3^{x} and y=(\frac{1}{3})^{x} have the same slope, except that the first is increasing and the other decreasing. The same thing happens with y=10^{x} and y=(\frac{1}{10})^{x}.
It would be as if we took the first one and reflected around the y axis to generate the second.
Here we can see that (\frac{1}{3})^{x}=(3^{-1})^{x}=3^{-x}
That is, raising a number to -x is the same as raising its opposite to x.
