7.7.4 Relate the Domain of a Function to Its Graph

Algebra 17.7.4 Relate the Domain of a Function to Its Graph

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

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

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

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$ would bring in the most revenue.

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

How much revenue (in dollars) would they make?

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

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

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

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

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

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