How do I find out how to determine what Domain and range are reasonable for functions? Step by step
Danny's truck has a fuel tank with a capacity of 20 gallons of gas. The truck averages 17 miles per gallon of gas. The function M(g) = 17g represents the number of miles that Danny's truck travels on g gallons of gas. What domain and range are reasonable for the function?
To determine the domain and range of a function, follow these steps:
1. Understand the context: Read the problem or description of the function carefully to understand the situation it represents. In this case, the function M(g) represents the number of miles Danny's truck travels on g gallons of gas.
2. Determine the restrictions or limitations: Consider any constraints or limitations given in the problem. In this case, the truck has a fuel tank with a capacity of 20 gallons of gas. So, the number of gallons of gas (g) cannot exceed 20.
3. Identify the domain: The domain of a function refers to the set of possible input values for the independent variable. In this case, the independent variable is the number of gallons of gas (g). Since the truck's fuel tank has a capacity of 20 gallons, the reasonable domain for this function would be all real numbers between 0 and 20, inclusive. So, the domain is: 0 ≤ g ≤ 20.
4. Identify the range: The range of a function refers to the set of possible output values for the dependent variable. In this case, the dependent variable is the number of miles traveled (M). The truck averages 17 miles per gallon of gas, so for any value of g (number of gallons), the number of miles traveled (M) will be 17 times the number of gallons (M = 17g). Since there are no limitations or constraints on the number of miles traveled, the reasonable range for this function would be all real numbers greater than or equal to 0. So, the range is: M ≥ 0.
Therefore, the domain is 0 ≤ g ≤ 20 and the range is M ≥ 0.