# How do you graph y=-sqrtx, compare it to the parent graph and what is the domain and range?

Dec 3, 2017

Check the explanation for the answer because my answer is much too long for this box!

#### Explanation:

To graph $y = - \sqrt{x}$ draw the parent graph first. The parent graph is this:
graph{sqrt(x) [-10, 10, -5, 5]}

Then, flip it over the x-axis, since the negative in $y = - \sqrt{x}$ is outside the square root symbol. If it was inside the square root symbol, however, the graph would be flipped over the $y$-axis.

$y = \sqrt{- x}$ looks like this:
graph{sqrt(-x) [-10, 10, -5, 5]}

While your equation ($y = - \sqrt{x}$) looks like this:
graph{y=-sqrt(x) [-10, 10, -5, 5]}

Compare it to the parent graph by noticing its reflections and transitions and writing them down as well.

The domain and range of the parent graph would be this:
D: (0,+∞)
R: (0,+∞)

The domain and range of the equation that you had provided
($y = \sqrt{- x}$) would be this:
D: (0,+∞)
R: (0,-∞)

Hope that helped!