Is it 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

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

Front

What is a mapping in the context of functions?

Back

A mapping is a way to describe a function, showing how each element of the domain (input) is paired with an element of the codomain (output).

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if for every x-coordinate, there is only one corresponding y-coordinate.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. Each input must map to exactly one 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.

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 is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x produces 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 the set of points {(1, 2), (1, 3)}, where the input 1 has two different outputs.