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

Jan 1, 2017

See explanation.

#### Explanation:

Domain

The domain of a function is the largest subset of $\mathbb{R}$ for which the function's formula is defined.

Given function is a polynomial, so there are no limitations for the values of $x$. This means that the domain is $D = \mathbb{R}$

Range

The range is the interval of values which a function takes.

A quadratic function with a positive coefficient of ${x}^{2}$ takes all values in an interval [q;+oo) where $q$ is the $y$ coefficient of the function's vertex.

$p = \frac{- b}{2 a} = \frac{2}{2} = 1$

$q = f \left(p\right) = {1}^{2} - 2 \cdot 1 + 3 = 1 - 2 + 3 = 2$

The function's range is [2;+oo)