Question

(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

Answer 1

The correct option is 1.

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.