The equation of the function graphed is y = (4) ˣ - 2
How to find the equation
The equation is an exponential function which is written of the form
y = a (b) ˣ
From the graph we translate the figure up 2 units to return to the preimage. At this point we have that points (0, 1) and (1, 4) on the graph
so that using (0, 1)
y = a (b) ˣ (b exponent of 0 is 1)
1 = a 1
a = 1
Using (1, 4) to solve for b
y = a (b) ˣ
4 = 1 (b) (b exponent of 1 is b)
b = 4
The equation is y = (4) ˣ then will translate it to revere the initial procedure
y = (4) ˣ - 2