A function that models the profit for a new pet-monitoring system shows that there is no profit made until the price reaches 95 dollars per unit, a maximum profit at a price of 140 dollars per unit, and no profit at a price over 180 dollars per unit. Which graph models the function?
Answer
A
Image with description On a coordinate plane, the x-axis ranges from 0 to 200 in increments of 10, and y-axis ranges from 0 to 200 in increments of 10. A curve increases, then passes through the point 0 comma 185, and then decreases through the point 95 comma 0.
B
Image with description On a coordinate plane, the x-axis ranges from 0 to 200 in increments of 10, and y-axis ranges from 0 to 2,000 in increments of 100. A curve passes through the point 100 comma 1,500, decreases to the point 140 comma 0, and then increases through the point 180 comma 1,500.
C
Image with description On a coordinate plane, the x-axis ranges from 0 to 200 in increments of 10, and y-axis ranges from 0 to 2,000 in increments of 100. A curve passes through the point 100 comma 400, increases to the point 140 comma 2,000, and then decreases through the point 180 comma 400.
D
Image with description On a coordinate plane, the x-axis ranges from 0 to 200 in increments of 10, and y-axis ranges from 0 to 200 in increments of 10. A curve passes through the point 0 comma 95, decreases to the point 180 comma 0, and then increases.
Explanation
The profit is zero at prices of $95 and $180, so the graph should cross the horizontal axis at those prices. Profit reaches its maximum at $140, so the curve should peak at x = 140 between those two break-even prices. Choice C shows a curve rising to a maximum at (140, 2,000) and then falling, matching that pattern; its listed points at $100 and $180 are consistent with the described curve.
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