Question

Give an example of a function with a domain of (Negative Infinity, 0 Give an example of a function with a range of [4, Infinity)

Answer 1

Function
`f(x)=√(-x)` has domain
`(-\infty ,0]`

Function
`f(x)=x^2+4` has range
`[4 ,\infty )`

Explanation:

Domain of the function
`f(x)` refers to the values of
`x` and the range refers to the values that the function
`f(x)` takes for various values of
`x`.

Consider a function
`f(x)=√(-x)`

As value within the square root is non-negative.

`-x\geq 0\\x\leq 0`

So, domain is
`(-\infty ,0]`

Now, consider a function
`f(x)=x^2+4`

Clearly,

`x^2\geq 0\\x^2+4\geq 4\\f(x)\geq 4`

So,

range of
`f(x)` is
`[4 ,\infty )`