# How do you find the domain and range of -x^2+7?

Jan 14, 2018

Domain: $x \in \mathbb{R}$
Range: $\left\{y | y \le 7\right\}$

#### Explanation:

Finding the Domain
The domain is where the function is defined in terms of real numbers. This function is always defined, so the domain is all real numbers, $\mathbb{R}$.

Finding the Range
The range is the possible values that the function takes on. If we consider the function as a parabola, we can see that it will be concave downwards ($\cap$) because of the negative leading coefficient

This means that the range will be $- \infty$ to whatever the vertex of the parabola is. The vertex of the parabola of $- {x}^{2}$ is at $\left(0 , 0\right)$, and since our function is that same function but translated $7$ units up, our vertex will be at $\left(0 , 7\right)$. This means that the range of the function is from $- \infty$ to $7$:
$\left\{y | y \le 7\right\}$