Question

Consider a function that describes how a particular car's gas mileage depends on its speed. What would an appropriate domain for this function be? Choose the correct answer below. A. An appropriate domain would be 0 to 50 miles per gallon because the gas mileage is the independent variable of the function, and the domain consists of all reasonable values of the independent variable. B. An appropriate domain would be times from 0 to 10 minutes because the time is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable. C. An appropriate domain would be 0 to 100 miles per hour because the speed is the independent variable of the function, and the domain consists of all reasonable values of the independent variable. D. An appropriate domain would be 0 to 100 miles per hour because the speed is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable. E. An appropriate domain would be 0 to 50 miles per gallon because the gas mileage is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable.

Answer 1

In the given function, the speed of the car is the independent variable, and gas mileage is the dependent variable. Therefore, a reasonable domain for this function would be from 0 to 100 miles per hour, considering that most cars do not routinely exceed this speed.

Step-by-step explanation:

The function domain that describes how a car's gas mileage depends on its speed has speed as the independent variable, and gas mileage as the dependent variable. In a function, the independent variable represents inputs in the domain, and that is speed in this case.

Your options in the question reflect various scenarios, but the correct answer is option C: 'An appropriate domain would be 0 to 100 miles per hour because the speed is the independent variable of the function, and the domain consists of all reasonable values of the independent variable.' This answer is on the basis that most cars do not exceed speeds of 100 miles per hour in regular circumstances.

Remember, in a function, the domain constitutes all possible values that the independent variable can take. In this case, these are speeds that the car can attain, and not the gas mileage it can provide.

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