Question

Complete the table of values for the function f(x) = (1/3)x for a, b, and c. x : -2, -1, 0, 1, 2. f(x) : a, b, c, 1/3, 1/9

Answer 1

Answer: below

Explanation:

Answer 2

Given:

The function is

`f(x)=\left((1)/(3)\right)^x`

To find:

The missing values for a, b, and c in the given table.

Solution:

We have,

`f(x)=\left((1)/(3)\right)^x`

At x=-2,

`f(-2)=\left((1)/(3)\right)^(-2)`

`a=\left(3\right)^(2)`
`\left[\because \left((a)/(b)\right)^(-n)=\left((b)/(a)\right)^(n)\right]`

`a=9`

At x=-1,

`f(-1)=\left((1)/(3)\right)^(-1)`

`b=\left(3\right)^(1)`
`\left[\because \left((a)/(b)\right)^(-n)=\left((b)/(a)\right)^(n)\right]`

`b=3`

At x=0,

`f(0)=\left((1)/(3)\right)^(0)`

`c=1`
`\left[\because a^0=1, a\\eq 0\right]`

Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.