Function or Not a Function

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, typically representing a relationship between two sets.

Front

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

Back

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

Front

What is an ordered pair?

Back

An ordered pair is a pair of elements (x, y) where 'x' is the first element and 'y' is the second element.

Front

How can you determine if a relation is a function using a graph?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function by checking if any vertical line crosses the graph more than once.

Front

What is a domain in the context of functions?

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 a range in the context of functions?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it assigns a unique output to each input, meaning no two different inputs produce the same output.

Front

What is a mapping diagram?

Back

A mapping diagram is a visual representation that shows how each element of the domain is paired with an element of the range.