Exploring the Concept of Functions in Mathematics

What is the purpose of an input-output table in math?

• To display a list of numbers

• To calculate the sum of numbers

• To show the relationship between inputs and outputs

• To compare different mathematical operations

In the vending machine analogy, what does the input represent?

• The time you wait

• The money or selection you input

• The product you receive

• The machine itself

What happens if you input the same number into a function multiple times?

• You get different outputs each time

• The function changes its rule

• The function stops working

• You get the same output each time

Why is the vending machine not considered a function if it gives different products for the same selection?

• Because it is out of stock

• Because it is too slow

• Because it does not follow the rule of a function

• Because it is broken

What indicates that an input-output table is not a function?

• The inputs are all different

• An input is paired with different outputs

• The table has more than five rows

• The outputs are all the same

In the example of a non-function table, what was the issue with the input '4'?

• It was not used

• It was paired with different outputs

• It was paired with zero

• It was paired with the same output

Is it acceptable for different inputs to produce the same output in a function?

• Only if the inputs are consecutive numbers

• Only if the outputs are prime numbers

• Yes, it is acceptable

• No, it is not acceptable

What is the key rule for an input-output table to be considered a function?

• Each input must produce a unique output

• Each input must produce the same output every time

• Each output must be a prime number

• Each input must be a positive number

In the final example, why is the table with inputs '5' and '-5' considered a function?

• Because they are both positive numbers

• Because they are both negative numbers

• Because they produce different outputs

• Because they produce the same output

What is the definition of a function as recapped in the video?

• An output always produces the same input

• An output always produces a different input

• An input always produces a different output

• An input always produces the same output