(04.07)
which of the following exponential functions goes through the points (1, 6) and (2, 12)? (2 points)

f(x) = 3(2)x
f(x) = 2(3)x
f(x) = 3(2)−x
f(x) = 2(3)−x

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

Put x=1

Put x=2

Both points are satisfied by this function therefore the correct option is 1.

The second function is

Put x=1

Put x=2

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.

a negative exponent is translated as follows:

so, we have