Functions and Relations

Front

What is a function?

Back

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

Front

What is a relation?

Back

A relation is a set of ordered pairs, which can include functions but does not require that each input has only one output.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once.

Front

What does the equation y = x + 5 represent?

Back

This equation represents a linear function where the output (y) increases by 1 for every increase of 1 in the input (x), starting from 5.

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

What is an example of a function?

Back

An example of a function is y = 2x + 3, where each x-value has one corresponding 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 {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

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

Back

For a relation to be a function, each input must be paired with exactly one output.

Front

What is a mapping in the context of functions?

Back

A mapping shows how each element of one set (domain) is paired with elements of another set (range).

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function can have multiple outputs for a single input.