It is an extremely useful skill to be able to define functions from the information given in a word problem. But, it’s also something most people find difficult.
First, you’ll learn how to translate word problems into linear functions,
Rule
Example 1
Find a function for the price of base jump insurance with a fixed price of
The word problem has indicated that there is a fixed cost to you, no matter how many times you jump, in addition to an amount that changes with each jump you take. If you set
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Example 2
Let’s say you have earned your driver’s license, and you are going on a trip and need to rent a car. You consider two types of rental agreements. The rental agreement “Smart Young 1” has a fixed payment of
In this case, you need to a function that represents the cost of each rental agreement, and plot them into the same coordinate system. Then, you need to make an assessment. In this case, to make the graph easier to read, you let
The fixed price is $
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The fixed price is $
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Inserting the functions into a drawing tool produces these graphs:
From the graphs, you can see that rental agreement “Smart Young 2” is the cheaper option if you’re driving 60 miles. Rental agreement “Smart Young 1” is cheaper if you’re driving less than 25 miles.