# What is the domain and range of #f(x) = -1 sqrt (1-x^2)#?

##### 1 Answer

Domain:

Range:

#### Explanation:

The domain of the function will only be influenced by the fact that the square root of a number will result in a *real value* **only** if said number is **positive**.

In other words, the possible values of

This condition is met when **Zero**, which means tha you need to find the interval(s) on which it is *positive*.

It's easy to see that for **negative**, which means that the interval of interest will actually be

Since the only values of

Now for the range of the function. Since the quadratic we've just looked at is equal to **zero** for **zero** and the point in which the quadratic has a *maximum value*.

More specifically,

At point

Therange of the function will thus be

graph{-sqrt(1-x^2) [-10, 10, -5, 5]}