Functions, Functions, Functions

Front

What makes a function special?

Back

Every input has only ONE output

Answer explanation

A function is defined as a relation where every input (x-value) corresponds to exactly one output (y-value). This means that for each input, there cannot be multiple outputs, making 'Every input has only ONE output' the correct definition.

Front

Is this mapping a function or not a function?

Back

Not a Function

Answer explanation

This mapping is not a function because it assigns the same input to multiple outputs, violating the definition of a function where each input must correspond to exactly one output.

Front

What are the y values or outputs called in a function?

Back

Range

Answer explanation

All of the y values or outputs in a function are collectively referred to as the 'range'. The range represents the set of possible output values, distinguishing it from the domain, which refers to the input values.

Front

All of the x values or inputs are called what?

Back

Domain

Answer explanation

All of the x values or inputs in a function are collectively referred to as the 'domain'. The domain represents the set of possible inputs for the function.

Front

Is the relation a function? Why?

Back

No, because the x-value 11 has two y-values paired with it.

Answer explanation

No, because the x-value 11 has two y-values paired with it. A function requires that each x-value corresponds to exactly one y-value, and this condition is violated in this case.

Front

Is the mysterious mapping a function?

Back

Function

Answer explanation

This mapping is a function because each input is associated with exactly one output. In a function, no input can map to multiple outputs, which is satisfied here.

Front

Is this graph a function or not a function?

Back

Function

Answer explanation

The graph is a function because each input (x-value) corresponds to exactly one output (y-value). This satisfies the definition of a function, confirming the correct choice is 'Function'.

Front

Is the mysterious graph a function or not a function?

Back

Function

Answer explanation

The graph is a function because each input (x-value) corresponds to exactly one output (y-value). This satisfies the definition of a function, confirming the correct choice is 'Function'.

Front

Is this table a function or not a function?

Back

Not a Function

Answer explanation

A table is not a function if any input (x-value) corresponds to more than one output (y-value). If there are repeated x-values with different y-values, it fails the vertical line test, making it 'Not a Function'.

Front

Is this graph a function?

Back

Not a Function

Answer explanation

The graph is not a function because it fails the vertical line test; a vertical line intersects the graph at more than one point, indicating that a single input corresponds to multiple outputs.