Unit 5: Identifying Functions (3)

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean for a mapping to represent a function?

Back

A mapping represents a function if each input is paired with exactly one output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an example of a function?

Back

f(x) = x^2 is a function because for each input x, there is one output.

Front

What is an example of a relation that is not a function?

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 has two different outputs.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each output is paired with exactly one input.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs in a function.

Front

What does it mean if a graph is not a function?

Back

If a graph is not a function, it means that at least one input is associated with multiple outputs.