Question

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

Answer 1

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!