Identifying Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

How can you identify if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (input) with different second elements (outputs).

Front

What does it mean for an input to have multiple outputs in a relation?

Back

If an input has multiple outputs, the relation is not a function.

Front

Given the ordered pairs {(2, 3), (3, 4), (2, 5)}, does this represent a function?

Back

No, because the input '2' corresponds to two different outputs (3 and 5).

Front

Given the ordered pairs {(1, 2), (2, 3), (3, 4)}, does this represent a function?

Back

Yes, each input corresponds to exactly one output.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs, showing how each input is connected to its output.

Front

In a mapping diagram, what indicates that a relation is a function?

Back

Each input must connect to only 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 is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.