Question

What are the domain and range of the function?
f(x) = -3√x

Answer 1

Domain:
`x\geq 0`

Range:
`y\leq 0`

Explanation:

Recall that the domain of a function is the values that x can be, while the range of a function is the values that y can be.

Let's take a look at one part of the function:
`√(x)`.

The square root of any positive number does exist. It may not be rational, but it exists. The square root of zero also exists -- it's zero.

However, the square root of a negative number will never exist - it's imaginary. So, x cannot be negative as long as it is under the radical.

The domain is:
`x\geq 0`

Now, to find the range, let's look at the coefficient: -3.

A negative number times a negative number is positive. A negative number times a positive number is negative.

However, x can never be negative, so no matter what real value you plug in for x, you will always be multiplying -3 by a positive number (or zero).

Since zero times any number is zero, and a positive number times a negative number is a negative number, y will always be either equal to zero or negative.

So, the range is:
`y\leq 0`