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

1 Answer
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!