So I'm supposed to find an equation that fits the graph, but the problem is, I have no idea how, and since the key only contains the answer, I'd like a step-by-step solution...
So far I have come up with an equation $y= 4a^{(x+4)} -1$, but that yields $a=\sqrt{\frac{1}{3}}$ for me, and is different from the answer $y=(\frac{1}{3})^{(x+4)} + 2$. Where did I go wrong.
First thing about exponential function is, its values/graph approximates zero, so the whole graph is lifted by two (that's the $+2$ there).
Once we subtract the 2, we see that the graph is going through one at point $x=-4$, but should go at zero, so the graph is moved by 4 to the left, hence the $+4$, (becuase if $x=-4$, then $x+4=0$). And we move it to the right.
The last thing (or two) we notice is the translated graph going through point $(-1,3)$ and $(-2,9)$, therefore we need to find base a, for which this is true, and that is $1/3$.
So, putting all of that together gives us $y=\frac 1 3^{(x+4)}+2 $
EDIT: The situation would be more complicated if there was a multiplicative constant, fortunately there is not. But in case there would be, you need to be looking for known exact values and determining individual components of the exponential function, the base for instance as ratio of two values.