Question

A science teacher wrote the table of values below.

Which function models the data in the table?

A. f(x)= 1/x , x =/ 0

B. f(x)= log 1/x^2 , x =/ 0

C. f(x)= log 1/x , x =/ 0

D. f(x)= 1/x^2 , x =/ 0

Answer 1

C. f(x)= log 1/x^2 , c=/ 0

Answer 2

C. f(x)= log 1/x , x =/ 0.

Explanation:

Given : A science teacher wrote the table of values below.

To find : Which function models the data in the table.

Solution : We have given table with x and f(x ).

We can see from table if x =
`(1)/(10)` then f(x) =1

By logarithm rule : log (10) = 1 , log (100) = 2.

Substitute the values of x in f(x)=
`log(1)/(x)`.

If x =
`(1)/(10)` .

f(x)=
`log(1)/(((1)/(10)))`.

We can write it f(x) = log(10) = 1

If x =
`(1)/(100)` .

f(x)=
`log(1)/(((1)/(100)))`.

We can write it f(x) = log(100) = 2

Therefore, C. f(x)= log 1/x , x =/ 0.