Find the exponential function f(x)=a^x whose graph is given. Points (0,1) and (2,9)
To find the exponential function f(x)=a^x given the points (0,1) and (2,9), we need to substitute these points into the equation and solve for a.
From the point (0,1):
f(0) = a^0 = 1
1 = a^0
1 = 1
This tells us that a = 1.
From the point (2,9):
f(2) = 1^2 = 9
1 = 9
9 = 9
Therefore, the exponential function f(x) = 1^x is given by f(x) = 1^x = 1^x.