Answer:
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.
Step-by-step explanation:
We are given a function f(x) by:
[tex]f(x)=3\cdot (\dfrac{1}{3})^x[/tex]
This means that:
[tex]f(1)=1[/tex]
[tex]f(2)=3\cdot (\dfrac{1}{3})^2\\\\\\f(2)=\dfrac{1}{3}\\\\i.e.\\\\f(2)=\dfrac{f(1)}{3}[/tex]
Similarly, we get:
[tex]f(3)=\dfrac{f(2)}{3}[/tex]
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. (-∞,∞)
[tex](\dfrac{1}{3})^x>0\\\\This\ implies\\\\3\cdot (\dfrac{1}{3})^x>0\\\\i.e.\\\\f(x)>0[/tex]
Hence, the range is all real numbers greater than 0.
- The graph is non-linear as it is a exponential decay curve.
