Function or Not

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

What is the definition of input in a function?

Back

An input is a value that is fed into a function, typically represented as 'x'.

Front

What is the definition of output in a function?

Back

An output is the result produced by a function for a given input, typically represented as 'y'.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input is associated with exactly one output.

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 the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

Is the mapping {(1,2), (2,3), (3,4)} a function?

Back

Yes, this mapping is a function because each input has exactly one output.

Front

Is the mapping {(1,2), (1,3), (2,4)} a function?

Back

No, this mapping is not a function because the input '1' has two different outputs (2 and 3).

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x gives a unique output.

Front

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

Back

An example of a relation that is not a function is the set of points {(1,2), (1,3)}, where the input '1' has two outputs.