Question

Complete the table of values for the function. f(x) = ( 1 /3)^x A = b= C=

Answer 1

The completed table of values is:

x J(x)

-2 9

-1 3

0 1

1 1/3

2 1/9

To complete the table of values for the function
`f(x) = (1/3)^x`, we need to substitute the given values of x into the function and find the corresponding values of f(x).

Let's go through each value of x and find its corresponding value of f(x):

For x = -2:

We substitute -2 into the function:

`f(-2) = (1/3)^(-2)`

Since a negative exponent means taking the reciprocal, we have:

`f(-2) = (3/1)^2`

`f(-2) = 9/1`

So, the value of a is 9.

For x = -1:

We substitute -1 into the function:

`f(-1) = (1/3)^(-1)`

Again, taking the reciprocal of a negative exponent gives:

`f(-1) = (3/1)^1`

`f(-1) = 3/1`

The value of b is 3.

For x = 0:

We substitute 0 into the function:

`f(0) = (1/3)^0`

Any number raised to the power of 0 is equal to 1, so:

f(0) = 1

The value of c is 1.

For x = 1:

We substitute 1 into the function:

`f(1) = (1/3)^1`

The value of 1/3 raised to the power of 1 is simply 1/3:

f(1) = 1/3

For x = 2:

We substitute 2 into the function:

`f(2) = (1/3)^2`

To find
`(1/3)^2`, we multiply 1/3 by itself:

`f(2) = (1/3) * (1/3)`

f(2) = 1/9

The value of f(2) is 1/9.