How do you graph y=−√x, compare it to the parent graph and what is the domain and range?

1 Answer
kat
Dec 3, 2017

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

Explanation:

To graph y=−√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=−√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=√−x looks like this:
graph{sqrt(-x) [-10, 10, -5, 5]}

While your equation (y=−√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=√−x) would be this:
D: (0,+∞)
R: (0,−∞)

Hope that helped!

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