Question

Which of these statements is true for f(x)=(1/2)^x

Answer 1

The correct answer is C: The y-intercept is (0,1).

Answer 2

The correct option is C.

Explanation:

The general exponential function is

`f(x)=ab^x`

Where, a is initial value and b is growth factor.

The given function is

`f(x)=((1)/(2))^x`

Here
`b=(1)/(2)<1`, therefore it is a decay function. In other words, the given function always decreases.

The given function is defined for all real numbers, therefore the domain of the function is all real number.

Put x=0, to find the y-intercept.

`f(x)=((1)/(2))^0=1`

The y-intercept of the function is at (0,1). Therefore option C is correct.

`((1)/(2))^x>0`

`f(x)>0`

Therefore the range of the function is y>0.