# How do you graph y=sqrtx-2 and what is the domain and range?

Feb 21, 2018

See below.

#### Explanation:

The graph looks like this:

graph{sqrt(x)-2 [-10, 10, -5, 5]}

The domain is all possible values of $x$ that give out a defined value of $f \left(x\right)$.

Here, $y$ will be undefined if $x < 0$, as the square root function cannot, really, have an input below $0$

So $x \ge 0$.

In interval notation, the domain is $\left[0 , \infty\right)$.

The range is all possible outputs of $f \left(x\right)$.

Since a square root function does not give an answer above $0$, the range of $\sqrt{x}$ is $y \ge 0$. However, since the above function is $\sqrt{x} - 2$, the range is $y \ge - 2$, or in interval notation:

$\left[- 2 , \infty\right)$.