Question

How do you find the domain and range of `y = sqrt(x+8)`?

Answer 1

Domain is `x >= -8`

Range is `y >= 0`

Explanation:

Let's take a look at the equation first.

`y = sqrt(x+8)`

For the domain, we're interested in the values of x that give a "valid result".

In other words, we're looking for values of x that won't "break" the equation.

We notice that `x+8` is inside of a square root. We also know that anything inside of a square root must be non-negative, since you can't take the square root of a negative number.

Therefore, we can set this up.

`x+8 >=0`

subtract 8 from both sides to get,

`x >= -8` , which is the domain.

Now, for the range.

We know that the square root of a number cannot be negative. This is the same for function such as `x + 8`. So, we get:

`y >= 0`

It's worth noting here that the square root symbol is used to indicate only the positive root. For example,

`sqrt(4) = 2`

while if `x^2 = 4`, then `x = +-2`