Question

Which statement describe the function of f(x)=3(1/3)x check all that apply

Answer 1

The range of the function is all real numbers greater than 0.

As the domain values increase, the range values decrease.

Each successive output is the previous output divided by 3.

Answer 2

The correct statements are:

• Each successive output is the previous out[put divided by 3.

• As the domain value increases, the range value decreases.

• The range of the function is all real numbers greater than zero.

Explanation:

We are given a function f(x) by:

`f(x)=3\cdot ((1)/(3))^x`

This means that:

`f(1)=1`

`f(2)=3\cdot ((1)/(3))^2\\\\\\f(2)=(1)/(3)\\\\i.e.\\\\f(2)=(f(1))/(3)`

Similarly, we get:

`f(3)=(f(2))/(3)`

and so on.

• This means that each of the output is the previous output divided by 3.

• Also, when the domain increases the range decreases.

( Since, with each increasing values of x the function value is getting decreased by some factor of 1/3 )

• The function is defined for all the real values.

i.e. the domain is all the real numbers i.e. (-∞,∞)

• Also, we know that:

`((1)/(3))^x>0\\\\This\ implies\\\\3\cdot ((1)/(3))^x>0\\\\i.e.\\\\f(x)>0`

Hence, the range is all real numbers greater than 0.

• The graph is non-linear as it is a exponential decay curve.