# What is the domain and range of  f(x) = x^2-4x-7?

Jan 19, 2016

The domain is the set of all real numbers.
The range is $y \ge - 11$

#### Explanation:

The domain of a function is the set of possible $x$ values, and the range is the set of possible $y$ values.

In this example there is no restriction on the set of real values that $x$ can take on. There are no square roots or possible undefined values. Therefore the domain is the set of all real numbers.

To find the range, we need to find the vertex of the parabola.
$f \left(x\right) = {\left(x - 2\right)}^{2} - 4 - 7$

The vertex is $\left(2 , - 11\right)$ and because the bracketed term is positive all $y$ values will be greater than the $y$ value at the vertex.

The range is therefore $y \ge - 11$