Question

What are the domain and range of the function? f(x)=−4x√x

Answer 1

Domain x ≥ 0 Range y ≤ 0

Explanation:

Answer 2

`Domain = \x\,`

`Range=\\,y\,`

Explanation:

Notice that the Range of the function (x-values for which the function exists) is limited by the possible values of x inside the square root. For
`√(x)` to exist, x must be larger than or equal to zero (
`x\geq 0`)

So this gives us the description for building the Domain (what is called "set builder notation":

`Domain = \x\,`

Now for the Range, let's look into all the possible values that these
`x\geq 0` values of x can render:

`x\geq 0\\√(x) \geq 0\\x\,√(x) \geq 0`

but now, if we multiply both sides of the inequality by "-4", the direction of the inequality changes rendering;

`-4\,x\,√(x) \leq 0`

Since these are the possible values of the "y-coordinate", then we right the Range in set builder notation as:

`Range=\\,y\leq 0\`