How do you graph y=-2sqrt(x+1)y=−2√x+1, compare it to the parent graph and what is the domain and range?

1 Answer
Tony B
Jan 30, 2018

Range ->y in [0,-oo)→y∈[0,−∞)
Domain -> x in [-1,+oo)→x∈[−1,+∞)

Explanation:

For the solution not to enter the domain of complex numbers the content of the root must never be negative.

Thus the cut off is x>=-1 x≥−1

Deriving the 'cut off point'
The x+1x+1 'shifts' ( translate ) the xx left. In that the x-intercept is:

y=0=-2sqrt(x+1)y=0=−2√x+1

sqrt(x+1)=0√x+1=0

x=-1 x=−1

You can manipulate the given equation in such a way that you end up with a ul(color(red)("variant on ") +x=(-y)^2=(+y)^2. This has the form sub as it is a quadratice in y

However, the right hand side of y=-2sqrt(x+1) will allways be negative so y will always be negative. Thus you:
ul("only have the bottom half of the "sub)

color(blue)("In summery you have:")

The parent graph of y=x^2 is rotated clockwise pi/2 and then translated left by 1 on the x-axis. The multiplication by 2 makes it more narrow. The negative means you only have the lower part of the form sub ie y<=0

Tony B

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