Question

hich statement best describes the domain and range of p(x) = 6–x and q(x) = 6x? p(x) and q(x) have the same domain and the same range. p(x) and q(x) have the same domain but different ranges. p(x) and q(x) have different domains but the same range. p(x) and q(x) have different domains and different ranges.

Answer 1

`p(x)` and
`q(x)` have the same domain and the same range.

Explanation:

`p(x) = 6-x` and

`q(x) = 6x`

First of all, let us have a look at the definition of domain and range.

Domain of a function
`y =f(x)` is the set of input value i.e. the value of
`x` for which the function
`f(x)` is defined.

Range of a function
`y =f(x)` is the set of output value i.e. the value of
`y` or
`f(x)` for the values of
`x` in the domain.

Now, let us consider the given functions one by one:

`p(x) = 6-x`

Let us sketch the graph of given function.

Please find attached graph.

There are no values of
`x` for which p(x) is not defined so domain is All real numbers.

So, domain is
`(-\infty, \infty)` or
`x\in R`

Its range is also All Real Numbers

So, Range is
`(-\infty, \infty)` or
`x\in R`

`q(x) = 6x`

Let us sketch the graph of given function.

Please find attached graph.

There are no values of
`x` for which
`q(x)` is not defined so domain is All real numbers.

So, domain is
`(-\infty, \infty)` or
`x\in R`

Its range is also All Real Numbers

So, Range is
`(-\infty, \infty)` or
`x\in R`

Hence, the correct answer is:

`p(x)` and
`q(x)` have the same domain and the same range.