Answer: Choice B
min = -5
max = -0.5
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Step-by-step explanation:
Graph each inequality given on the same xy coordinate system. You should get what you see in the attached image below. The red shaded region represents all points that make every inequality mentioned to be a true statement. Points A, B, C are vertex points of the boundary region.
A = (2,6)
B = (5,3)
C = (2,3)
For each point A,B,C, plug in the (x,y) coordinates into the C(x,y) function given
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For point A, (x,y) = (2,6) so x = 2 and y = 6
C(x,y) = (1/2)*x - y
C(2, 6) = (1/2)*2 - 6
C(2, 6) = -5 we'll use this value later
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Repeat for point B = (5,3)
C(x,y) = (1/2)*x - y
C(5,3) = (1/2)*5 - 3
C(5,3) = -0.5 we'll use this value later
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Repeat for point C = (2,3)
C(x,y) = (1/2)*x - y
C(2,3) = (1/2)*2 - 3
C(2,3) = -2 we'll use this value later
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In the previous three sections above, we got the following outputs: -5, -0.5, -2
We see that -5 is the smallest and -0.5 is the largest
Therefore, -5 is the min and -0.5 is the max