Identify Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is the definition of 'not a function'?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

How can you tell if a mapping is a function?

Back

A mapping is a function if each input (x-value) has exactly one output (y-value).

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

What does it mean if a set of ordered pairs is a function?

Back

If a set of ordered pairs is a function, each first element (x-value) is paired with exactly one second element (y-value).

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, where each x-value corresponds to one y-value.

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 pairs {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Front

What is the significance of the Horizontal Line Test?

Back

The Horizontal Line Test determines if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

Front

What is a graph of a function?

Back

A graph of a function is a visual representation of the relationship between the input (x-values) and output (y-values) of the function.