# What is the domain and range of y=sqrt(5x+2)?

Nov 11, 2017

$x \ge - \frac{2}{5} , x \in \mathbb{R}$
$y \ge 0 , y \in \mathbb{R}$

#### Explanation:

The domain is the values of $x$ for which we can plot a value for $y$.
We cannot plot a value for $y$ if the area under the square root sign is negative since you cannot take the square root of a negative (and get a real answer.
To give us the domain:

let $5 x + 2 \ge 0$
$5 x \ge - 2$
$x \ge - \frac{2}{5} , x \in \mathbb{R}$

The range is the values of $y$ we get from plotting this function.
We get our lowest value when $x = - \frac{2}{5}$

Let $x = - \frac{2}{5}$
y=sqrt(5(-2/5)+2
$y = \sqrt{- 2 + 2}$

$y = \sqrt{0} = 0$
Any x value greater than -2/5 will give a bigger answer, and as $x \to \infty , y \to \infty$ also.

So the range is $y \ge 0 , y \in \mathbb{R}$