Functions

Front

What is a function?

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 vertical line test?

Back

The vertical line test is a method 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 graph to be a function?

Back

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

Front

What is a mapping in mathematics?

Back

A mapping is a relation that pairs each element of one set with an element of another set.

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 for every input x, there is a unique output.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.

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 the function.

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

What does it mean if a graph is not a function?

Back

If a graph is not a function, it means that at least one input is associated with more than one output.