Identifying functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

What is the definition of a relation that is not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

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

Back

A mapping is a function if each input (x-value) corresponds to exactly one output (y-value).

Front

Can a vertical line intersect a graph more than once for it to be a function?

Back

No, if a vertical line intersects a graph more than once, the relation is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

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.

Front

What is the significance of the 'x' values in determining if a relation is a function?

Back

The 'x' values must be unique; if any 'x' value is repeated with different 'y' values, it is not a function.

Front

How can you visually determine if a graph represents a function?

Back

You can use the vertical line test; if a vertical line crosses the graph at more than one point, it is not a function.

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.