# How do you find the domain and range of #y =sqrt (x^2 - 9)#?

##### 1 Answer

The domain is

The range is

#### Explanation:

One way to find it is by graphing it, and then looking for the

graph{sqrt(x^2-9) [-10, 10, -5, 5]}

It looks like the range is

The domain is

But let's solve this algebraically.

The square root function is only defined when the number or expression under the radical sign is greater than or equal to

Therefore,

Now, we set it *equal* to

Now we have these points. Let us call them boundary points of the real number line. So we have 3 intervals -

Just choose a point in each interval and substitute it into the original equation *including*, we get the domain is

For the range, just think about this - the lowest value a square root function can give is