Identifying Function Properties with Real-World Examples

This video tutorial explains the concept of functions, highlighting that a function is a relation where each input has exactly one output. It addresses common misconceptions, such as multiple inputs sharing the same output, which is still a function. The tutorial uses real-world examples like gumball machines and a parking garage to illustrate function properties, including one-to-one functions and constant rates of change. It concludes by analyzing these examples to identify function properties and clarify the concept of one-to-one functions.

What is a key characteristic of a function?

• Inputs and outputs are unrelated.

• Outputs can be random.

• Each input has exactly one output.

• Each input can have multiple outputs.

In the first gumball machine example, what does each quarter input yield?

• 4 gumballs

• 3 gumballs

• 1 gumball

• 2 gumballs

What is the cost of parking for 5 hours in the parking garage example?

• $15

• $9

• $12

• $18

What does 'one-to-one' mean in the context of functions?

• Each input can have multiple outputs.

• Each input has a unique output not shared with other inputs.

• Outputs can be shared among inputs.

• Inputs are unrelated to outputs.

Which property does the first gumball machine exhibit?

• It is not a function.

• It has a constant rate of change.

• It is not one-to-one.

• It has multiple outputs for one input.

Why is the second gumball machine not considered a function?

• It has a unique output for each input.

• It shares outputs among inputs.

• It gives multiple outputs for a single input.

• It has a constant rate of change.

Why is the parking garage example not one-to-one?

• Multiple inputs share the same output.

• It has a constant rate of change.

• The cost remains constant after a certain point.

• Each input has a unique output.