Relation and Function Flashcard

Front

What is a function?

Back

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

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 is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

What is the difference between a function and a relation?

Back

All functions are relations, but not all relations are functions. A function has a unique output for each input.

Front

What does a mapping diagram show?

Back

A mapping diagram visually represents the relationship between inputs and outputs, helping to identify if a relation is a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents 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

An example of a function is f(x) = x^2, where each input x has a unique output x^2.

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 if a relation is not a function?

Back

It means that at least one input is associated with more than one output.