When taking square roots, you can't take square roots of negative roots of negative numbers. So, what will work for the domain of u(x) is what makes u(x) zero or more. We can make an inequality for that.
u(x) ≥ 0.
9x + 27 ≥ 0 by squaring both sides
9x ≥ -27
x ≥ -3
So the domain of the function is when x ≥ -3 is true.
The quadrant that the graph will not go through is the second quadrant.
The reason is that the slope is positive and there was a translation 6 units down
<h3>How to know the quadrant the graph will not pass</h3>The quadrants are named in anticlockwise direction starting from the first which has x - positive and y - positive
The graph of y = 2x/3 is a graph with positive slope, moving through the third and first quadrant.
y = 2x/3 - 6 means a translation 6 units down and this pushed the line to get to the fourth quadrant
Hence the remaining quadrant that is untouched is the second quadrant
The graph is attached
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