Functions

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

How can you determine if a relation is a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method 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 does it mean for a mapping to be a function?

Back

A mapping is a function if each element in the domain (input) is paired with exactly one element in the codomain (output).

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 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.

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 non-function?

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An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Front

What is the definition of 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 definition of 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.