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y=3x²+6x+5 can be written y=3x²+6x+3+2, that is, y=3(x²+2x+1)+2.

So y=3(x+1)²+2. This has a minimum value of 2 when x+1=0, that is, when x=-1. So the minimum range is 2.

As x gets more positive or more negative, y becomes more positive, so the maximum range is plus infinity.

That means the range of y is 2 to infinity, which can be written [2,∞) or [2,∞].

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