Understanding Functions

The video tutorial explains the concept of a function, emphasizing that each input must have exactly one output. It provides examples of functions and non-functions. The tutorial then analyzes four statements to determine if they describe functions: revenue as a function of shoes sold, unemployment rate as a function of the year, miles traveled as a function of travel rate, and income as a function of height. The first three statements are identified as functions, while the last one is not.

What is a function in mathematical terms?

• A relation where each input has exactly one output

• A relation where each output has multiple inputs

• A relation where each output has exactly one input

• A relation where each input has multiple outputs

In the context of functions, what does 'input' refer to?

• The output of a function

• The variable that is manipulated

• The constant in a function

• The result of a function

What is the relationship between input and output in a function?

• Each output has exactly one input

• Each input has exactly one output

• Each output can have multiple inputs

• Each input can have multiple outputs

Which of the following is an example of a function?

• An input with two different outputs

• An input with no outputs

• An input with exactly one output

• An output with multiple inputs

Which statement correctly describes a non-function?

• Each input has exactly one output

• An input can have multiple outputs

• Each output has exactly one input

• An output can have multiple inputs

Why is the revenue of a shoe company a function of the number of shoes sold?

• Because each number of shoes sold results in exactly one revenue amount

• Because revenue can vary for the same number of shoes sold

• Because revenue is independent of the number of shoes sold

• Because each number of shoes sold can result in multiple revenue amounts

What is the output in the function of revenue based on shoes sold?

• Type of shoes

• Number of shoes sold

• Cost of shoes

• Revenue amount

How does the yearly unemployment rate qualify as a function of the year?

• Unemployment rate is independent of the year

• Unemployment rate can vary for the same year

• Each year has exactly one unemployment rate

• Each year can have multiple unemployment rates

Why is the number of miles traveled a function of the average rate of travel?

• Because rate can vary for the same distance

• Because the same rate can result in different distances

• Because each rate results in exactly one distance

• Because distance is independent of the rate

Why is a person's income not a function of their height?

• Because people of the same height can have different incomes

• Because income is independent of height

• Because height can vary for the same income

• Because each height results in exactly one income