Domain/Range and Absolute values

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Originally Posted by Skoz

1.) state the domain and range of each relation, then determine if the relation is a function.

a) y= -2(x+1)^2-3

The domain are all real x.
Remember that $(x+1)^2\geq 0 \implies -2(x+1)^2 \leq 0 \implies -2(x+1)^2 \leq -3$ so the range is $y\leq -3$ .

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b) y=1/x+3

The domain are all $x\not = 0$ .
As for the range we have $y>3 \text{ or }y<-3$ .
To see this picture the hyperbola $y=x$ and shift it up 3 units.

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c) 2sinx

The domain are all real x and remember that $-1\leq \sin x\leq 1 \implies -2\leq 2\sin x\leq 2$ .
Thus, range is $|y|\leq 2$ .