Functions and Relations

Front

What is a function in mathematics?

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, the graph is not a function.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y). Relations can be functions, but not all relations are functions.

Front

How can you determine if a graph is a function?

Back

To determine if a graph is a function, you can use the vertical line test. If a vertical line crosses the graph more than once, it is not a function.

Front

What does it mean for a graph to be 'not a function'?

Back

A graph is 'not a function' if there exists at least one x-value that corresponds to more than one y-value.

Front

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

Back

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

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value corresponds to only one y-value.

Front

What is a one-to-one function?

Back

A one-to-one function is a function in which each output is associated with exactly one input, meaning no two different inputs produce the same output.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same 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.