Need help pleaseeeeeeeeeeee???
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The region in the <em>x</em>-<em>y</em> plane is the set of points
The height of the solid falls between the <em>x</em>-<em>y</em> plane (for which <em>z</em> = 0) and the equation of the plane, <em>z</em> = 3<em>x</em> + 2<em>y</em>.
So the volume is
The domain is the set of all point where you can evaluate the function.
As you can see, the first piece is defined from -infinity to 2 (included).
The second piece is defined from 2 to 6 (excluded).
The third piece is defined from 6 (excluded) to +infinity.
So, the domain of the function is composed by all the real numbers which are not 6:
As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.
The second piece is constantly equal to 2, so it adds nothing.
The third piece spans the y axis from -2 to -infinity, so the range is