Functions and Relations

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 corresponding y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, then the graph is not a function.

Front

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y). A relation can be a function if it meets the criteria of having only one output for each input.

Front

What does it mean for a relation to be not a function?

Back

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

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a two-dimensional space, where x is the first element (input) and y is the second element (output).

Front

How can you determine if a set of ordered pairs is a function?

Back

To determine if a set of ordered pairs is a function, check if any x-value appears more than once. If it does, the set is not a function.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its corresponding output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that result from using the function.

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.