# What is the domain and range of #f(x) = x^3 - 3x + 2#?

##### 1 Answer

Sep 2, 2015

Domain and range are both

#### Explanation:

The domain is defined as the set of the points which you can give as input to the function. Now, "illegal" operations are:

- Dividing by zero
- Giving negative numbers to an even root
- Giving negative numbers, or zero, to a logarithm.

In your function, there are no denominators, roots or logarithms, so all values can be computed.

As for the range, you can observe that every polynomial

#\lim_{x \to -\infty} f(x)=-\infty# #\lim_{x \to +\infty} f(x)= +\infty#

And since polynomials are continuous functions, the range consists in all numbers from