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Relate the Domain of a Function to Its Graph

7.7.4 Relate the Domain of a Function to Its Graph

7.7.4 • Relate the Domain of a Function to Its Graph

Cool Down

This graph represents the revenue in dollars that a company expects if they sell their product for pp dollars.

A parabola on a coordinate grid. The horizontal-axis represents the product price in dollars and the vertical-axis represents the revenue in dollars. The x-axis scale is 2 and extends from 0 to 22. The y-axis scale is 500 and extends from 0 to 6,000.
1.

Based on this model, which price would generate more revenue for the company, $5$5 or $17$17?

$5$5, as it would generate about $3,700$3,700 in revenue. Charging $17$17 would bring in about $2,500$2,500.

2.

At what price (in dollars) should the company sell their product if they wish to make as much revenue as possible?

Based on the graph, a price of $10$10 would bring in the most revenue.

1010. Based on the graph, a price of $10$10 would bring in the most revenue.

3.

How much revenue (in dollars) would they make?

Based on the graph, a price of $10$10 would bring in about $5,000$5,000.

$5,000$5,000. Based on the graph, a price of $10$10 would bring in about $5,000$5,000.

4.

What is an appropriate domain for the function? Explain how you know.

Compare your answer: Your answer may vary, but here is a sample.

0≤p≤200≤p≤20, because the price has to be non-negative, and the company would earn negative revenue if the price were more than $20$20.