Input/Output Machines

Front

What is an Input/Output Machine?

Back

An Input/Output Machine is a mathematical model that takes an input, applies a function or rule, and produces an output.

Front

What does the expression 'T + 11' represent in an Input/Output Machine?

Back

The expression 'T + 11' indicates that for every input T, the output is obtained by adding 11 to T.

Front

How do you identify the function of an Input/Output table?

Back

To identify the function, observe the relationship between the inputs and outputs, and determine the rule that connects them.

Front

What is the rule if the output is obtained by multiplying the input by 3?

Back

The rule is 'multiply by 3', meaning for any input x, the output is 3x.

Front

How do you find a missing term in an Input/Output table?

Back

To find a missing term, use the identified function or rule to calculate the output or input that is not provided.

Front

What is the output if the input is 4 and the function is 'multiply by 3'?

Back

The output would be 12, since 4 multiplied by 3 equals 12.

Front

If the input is 5 and the output is 10, what could be a possible function?

Back

A possible function could be 'multiply by 2', since 5 multiplied by 2 equals 10.

Front

What is the significance of identifying the rule in an Input/Output Machine?

Back

Identifying the rule is crucial as it allows you to predict outputs for any given inputs and understand the relationship between them.

Front

How can you express a function in algebraic form?

Back

A function can be expressed in algebraic form using an equation that relates the input to the output, such as y = f(x).

Front

What does it mean to 'identify the missing term' in a sequence?

Back

Identifying the missing term involves determining the value that completes a pattern or sequence based on the established rule.