Functions

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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 the function can produce.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input value corresponds to exactly one output 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 a vertical line intersects the graph at more than one point, it is not a function.

Front

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

Back

A mapping is a function if every element in the domain is paired with exactly one element in the range.

Front

What is an example of a non-function relation?

Back

An example of a non-function relation is the set of points {(1,2), (1,3)}, where the input '1' corresponds to two different outputs.

Front

What is the significance of the ordered pairs in a function?

Back

Ordered pairs in a function represent the relationship between inputs and outputs, where the first element is from the domain and the second is from the range.

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 corresponds to only one output.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is paired with exactly one unique input, meaning no two different inputs produce the same output.