Identifying 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

What is the definition of ordered pairs?

Back

Ordered pairs are pairs of numbers (x, y) where 'x' is the first element (input) and 'y' is the second element (output).

Front

What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if no two different ordered pairs have the same first element.

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 more than once, then the graph is not a function.

Front

How can you determine if a graph is a function?

Back

You can determine if a graph is a function by using the vertical line test.

Front

What is the significance of the first element in an ordered pair?

Back

The first element in an ordered pair represents the input value (domain) of the function.

Front

What is the significance of the second element in an ordered pair?

Back

The second element in an ordered pair represents the output value (range) of the function.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but it cannot have the same input with different outputs.

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 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' is related to two different outputs.