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How do you find the important points to graph #y = -2 sqrt(x + 2)#?

Answer 1

Most important point is when #y=0#

This happens when #x=-2-> (-2,0)#

#x>=-2# otherwise the argument would become negative (not allowed).

Then you can set up a table with #x#'s chosen so that the argument becomes a square: E,g.: #x=-1->y=-2sqrt(-1+2)=-2->(-1,-1)# #x=2->y=-2sqrt(2+2)=-4->(2,-4)# #x=7->y=-2sqrt(7+2)=-6->(7,-6)# Etc. graph{-2sqrt(x+2) [-5.46, 14.54, -8.72, 1.28]}

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Answer 2

Nathan Axel

To graph the function ( y = -2\sqrt{x + 2} ), you can start by identifying the key points:

x-intercept: Set ( y = 0 ) and solve for ( x ).
y-intercept: Set ( x = 0 ) and solve for ( y ).
Vertex: The vertex occurs at the point where ( x + 2 = 0 ).
Additional points: Choose other values of ( x ) to find corresponding values of ( y ).

Once you have these points, plot them on a graph and sketch the curve of the function passing through them.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.