Question

Using a real world example, state the domain and range of the function or relationship. What are the practical things to consider when limiting the domain and range of a real world function?

Answer 1

To apply the domain and range in real-world settings, we take a function that represents a real-world situation and then analyze what the domain and range represent in the function. This allows us to apply the domain and range in a real-world setting.

Consider the real world problems:

1)Pablo charges $20 an hour to teach salsa dancing. What is the domain and range of how much money pablo can make off salsa dancing lessons.
Solution
The number of hours he teaches will go on the x-axis and the amount of money Pablo makes goes on the y axis.
The least amount of money he can make is $0 dollars because he can only make money and he can't go in debt.
The equation is y=20x because it costs $20 an hour and x represent the number of hours he teaches.
The domain is [o,∞) and the range is also [0,∞)

2)Jimmy has to fill up his car with gasoline to drive to and from
work next week. If gas costs $2.79 per gallon, and his car holds a maximum of 28 gallons, what is the
domain and range of the function?
Solution
The number of gallons of gas purchased will go on the x-axis and the costs of the gasoline goes on the y-axis.
Because the least amount of gas he can purchase is 0 gallons which is $0 then part of the function is 0≤x.
The most amount of money he can spend on gas is $78.12 which is the full 28 gallons.
This adds to the function making it 0≤x≤28. Then to complete the function because each gallon of gas cost $2.79 and x represents the amount of gas bought the equation is y=2.79x and 0≤x≤28.
The domain is [0,28] and the range is [0,78.12]

Practical things to consider when limiting the domain and range of a real world function are:
1. If no equation is given to model the situation, write an appropriate linear model for
the problem.
2. State the domain and range for the function – be specific with any limitations that
exist due to the nature of the data.
Remember that DOMAIN describes the values that x (or the independent variable) can
be in the problem and RANGE describes the values that y (or the dependent
variable) can be in the problem.