Which graph represents the function f(x) = –|x + 3|?

The function f(x)=-|x+3| is defined as follows:

for x+3≥0, that is for x≥-3,         f(x)=-(x+3)=-x-3

for x+3<0, that is for x<-3,         f(x)=-[-(x+3)]=x+3

Thus in the interval [-3, infinity) we draw the half line, or ray, (i) y=-x-3, 

and in the interval (-infinity, -3) we draw the half line y=x+3.

To draw y=-x-3, we can use the points (-3, 0)   and   (0, -3), 

to draw the line y=x+3 we can use the points (-3, 0)   and    (0, 3)

Notice that the points we used to draw the second line, are not in the domain of the line, that is why on (-3, infinity) the line is dashed, that is it does not exist there, but we can still use it for practical purposes of drawing the half line.

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