# What is the domain and range of y = x^2 + 7?

Jul 17, 2016

Domain: All real numbers Interval Notation: $\left(- \infty , \infty\right)$
Range: All values greater than or equal to seven Interval Notation: $\left[7 , \infty\right)$

#### Explanation:

Graph of $y = {x}^{2} + 7$: graph{x^2+7 [-17.7, 18.34, 3.11, 21.89]}

The domain accounts for all the $x$ values that are included in the function. The range accounts for all the $y$ values included in the function.

Looking at the graph, we can see that the function stretches endlessly in both directions left and right. So, the domain is all real numbers. The range, however, starts from the point of $7$, and increase there on. So, the range is all values from 7 and increasing.

There are different ways to go about stating the domain and range. What I included in the answer is called interval notation. Interval notation notes all values included in the function using parentheses and brackets. Brackets include the value, parenthesis do not.

For example:

$\left[5 , 10\right)$ Here, interval notation is present. It states that all values including $5$ all the way up to but not including $10$ are included in the function.