Answer:
The correct option is 1.
Step-by-step explanation:
If the exponential function passing through a point it means the points satisfies the function.
If the exponential functions goes through the points (1, 6) and (2, 12). It means the value of the function at x=1 is 6 and the value of the function at x=2 is 12.
The first function is
\(f(x)=3(2)^x\)
Put x=1
\(f(x)=3(2)^1=6\)
Put x=2
\(f(x)=3(2)^2=12\)
Both points are satisfied by this function therefore the correct option is 1.
The second function is
\(f(x)=2(3)^x\)
Put x=1
\(f(x)=2(3)^1=6\)
Put x=2
\(f(x)=2(3)^2=18\)
This equation does not satisfy the second point therefore the option 2 is incorrect.
Since the power is in negative, therefore at x=2 the value of function is in the fraction form, therefore options 3 and 4 are incorrect.
