Functions

Front

What is a function?

Back

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

Front

What is the definition of 'not a function'?

Back

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

Front

Given the relation {(1,5),(1,7),(3,9),(4,11)}, is it a function?

Back

No, because the input '1' is associated with two different outputs (5 and 7).

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once.

Front

What does the vertical line test indicate?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If a vertical line crosses the graph more than once, it is not a function.

Front

Is the set of ordered pairs {(2,3),(3,4),(4,5)} a function?

Back

Yes, because each input value is associated with exactly one output value.

Front

What is an example of a function?

Back

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

Front

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

Back

An example is the relation {(1,2),(1,3)}, where the input '1' has two outputs.

Front

What is the output value for the input 4 in the function represented by the table: Input: 1, 2, 3, 4; Output: 10, 11, 12, ?

Back

The missing output value is 13.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its output.