Laura has two large cylindrical barrels of solution in her chemical laboratory. The first barrel contains 900 liters of solution
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Answer:
see attached for a graph
Step-by-step explanation:
It looks like you want to plot a graph of the function. For a piecewise function like this one, the effort is divided into pieces. The "or equal to" part of the comparison symbol tells you the end value is included in that interval.
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For the piece between x=-8 and x=-6, you can find the y-values by evaluating the function for those x-values.
For x = -8: y = -1/2(-8) = 4.
For x = -6: y = -1/2(-6) = 3.
So, the left piece can be plotted by drawing a line segment between points (-8, 4) and (-6, 3).
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For the piece between x=-6 and x=1, you can do the same thing:
For x=-6: y = -(-6) -3) = 6-3 = 3
For x=1: y = -(1) -3 = -4
So, the right piece can be plotted by drawing a line segment between points (-6, 3) and (1, -4). We notice that (-6, 3) is already the end point of the first piece, so the function is continuous at x=-6. (Sometimes there is a discontinuity between pieces. Not here.)
You can also plot the right piece by recognizing it is a line with a y-intercept of -3 and a slope of -1. That is, point (0, -3) will be on that line, and it will have a "rise" of -1 for each "run" of 1 (to the right).
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A graph is shown. We have made the pieces different colors, so you can see what they are. And we have plotted a filled dot at (-6, 3) to indicate that point is part of the function definition. (The dot is unnecessary.)
