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Answer:
A.
- intercepts: prices at which profit is zero
- maximum: price at which profit is maximum
- increasing: x < 5, where increasing price means increasing profit
- decreasing: 5 < x, where increasing price means decreasing profit
B. 20 dollars per dollar, the rate of increase of profit with respect to price changes
C. 0 ≤ x ≤10
Step-by-step explanation:
Part A: The description of the graph tells you that each point on the graph represents (price, profit). So, x-intercept points that are (price, 0) represent prices at which profit is zero. The point (price, maximum) = (5, 160) represents the price at which profit is maximized.
The curve is increasing to the left of the maximum, on the interval x < 5, and is decreasing to the right of the maximum, on the interval 5 < x. These are the intervals where increasing prices result in increasing and decreasing profits, respectively.
Part B:
The average rate of change between (2, 100) and (5, 160) is given by the slope formula:
m = (y2 -y1)/(x2 -x1) = (160 -100)/(5 -2) = 60/3 = 20 . . . . dollars per dollar
On average company profit increases by $20 for each $1 increase in the price of its pencils.
Part C:
Prices are not usually negative, so the domain is likely constrained to 0 ≤ x. The price could be set high enough to result in negative profit, but that is not a practical choice. So, the upper end of the reasonable domain is x ≤ 10.
The reasonable constraints on the domain are those than ensure profit is non-negative: 0 ≤ x ≤ 10.
