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Investigation 2: Whale-watching Tours

Step F

Analyze the graph of the new function and compare it to the linear functions you have already graphed in steps B and D. Note: this new function, h(x), is a quadratic since it is the combination of two linear functions. The graph is shaped like a parabola and has a maximum value (IE: a maximum profit). 

The domain is 

{x / x ? R}. 

However within the context of the problem, this domain won't work. Recall in step D you found that the tour couldn't have more than 40 extra passengers. Hence the domain, within the context of the problem, is

. 

The range, which represents the total revenue, can be found by locating the vertex. The y-coordinate of the vertex will be the greatest revenue possible. Note also that the lowest possible revenue will be $0. You should now be able to find the range.