Understanding Practical Domain and Range

This video lesson covers the concepts of practical domain and range in functions, using a real-world example of a gas station. It explains how to determine the input and output variables, and how to calculate the practical domain and range based on the constraints of the situation. The lesson concludes with a graphical representation of the cost function, illustrating the relationship between the number of gallons and the cost.

What is the practical domain of a function?

• The range of the function

• All possible values for the input variable

• The set of all real numbers

• All possible values for the output variable

In the gas station example, what does the input variable 'n' represent?

• The cost of gas

• The total distance traveled

• The price per gallon

• The number of gallons of gas

What is the maximum number of gallons the car's tank can hold in the example?

• 20 gallons

• 25 gallons

• 15 gallons

• 30 gallons

What is the practical domain for the number of gallons of gas?

• n must be between 0 and 20, inclusive

• n must be exactly 10

• n must be greater than 20

• n must be less than 0

What does the output variable represent in the gas station example?

• The number of gallons of gas

• The cost in dollars

• The total distance traveled

• The price per gallon

What is the practical range of the cost function in the example?

• From 0 to 50 dollars

• From 20 to 76.6 dollars

• From 0 to 100 dollars

• From 0 to 76.6 dollars

If you purchase 20 gallons of gas, what would be the cost?

• 20 dollars

• 100 dollars

• 50 dollars

• 76.6 dollars

Why doesn't it make sense to graph the function beyond an input of 20?

• Because the price per gallon changes

• Because the function is undefined

• Because the tank can only hold a maximum of 20 gallons

• Because the cost becomes negative

What happens to the output when there is a restriction on the input?

• The output becomes negative

• The output is also restricted

• The output remains constant

• The output becomes infinite

What is the significance of the graphical representation in understanding the function?

• It shows the function's behavior beyond the practical domain

• It demonstrates the function's behavior for negative inputs

• It highlights the constraints on input and output values

• It provides the exact cost for any number of gallons