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It seems like the line y = 1 is a horizontal asymptote.
Apart from that, it looks like an exponential function,
so my first guess would be: f(x)= 1+ a^x.
Maybe if you read off a few points on the graph, you could determine a.
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is it 2^x+2 ?
OOps, the unit is 2 on the axes...so it is f(x)=2+a^x
It looks like a^x, but since the left sides converges towards 2 and not 0 it looks more like:
y = 2+c*a^x
y(2) seems to be about 6
y(0) seems to be about 2.5
y(0) = 2.5 => 1 + c*a^0 = 1 + c
c = 1.5:
y(2) = 1 + 1.5*a^2 = 6
1.5*a^2 = 5
a = sqrt( 5/1.5 ) ~ 1.8
all in all,
y = 2 + 1.5 * 1.8^x
Now, let's see if I can read off the number a: if I move it down 2 units, it goes through (0,1). Also it would go through (2, 4), so a²=4/1=4. That means a=2.
I think you have found the answer already!
@BenjaminEE: seems you made an error reading off the value for y=0... (unit = 2 on the axes)