Below is the graph of , where and are integers. Find .

Two of the points on the graph are (2, -2)  and (3, -8)

f(x)  =  a^x/b

(2, -2)   --->   a²/b  =  -2     --->   a²  =  -2b     --->    a²/-2  =  b

(3, -8)   --->   a³/b  =  -8     --->   a³  =  -8b     --->    a³/-8  =  b

Setting the first equation equal to the second:     a²/-2   =   a³/-8 

Multiplying both sides by -8:                               4a²   =   a³

Dividing both sides by  a²  (This step is allowed provided that a²  ≠ 0):       4  =  a

Since  a²/b  =  -2  and  a  =  4:  16/b  =  -2     --->   b  =  -8

Now, find a + b: