Question

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

Answer 1

Answer:

Domain x ≥ 0 Range y ≤ 0

Step-by-step explanation:

Answer 2

Answer:

$Domain = \{x\,|\,x\geq 0\}$

$Range=\{\,y\,|\,y\leq 0\}$

Step-by-step 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 $\sqrt{x}$ 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":

$Domain = \{x\,|\,x\geq 0\}$

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

$x\geq 0\\\sqrt{x} \geq 0\\x\,\sqrt{x} \geq 0$

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

$-4\,x\,\sqrt{x} \leq 0$

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

$Range=\{\,y\,|\,y\leq 0\}$