5.1: Is This a Function? (Ordered Pairs)

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for every input (x).

Front

What is a relation?

Back

A relation is a set of ordered pairs, which may or may not assign exactly one output for each input.

Front

True or False: All functions are relations.

Back

True. Every function is a relation, but not all relations are functions.

Front

True or False: All relations are functions.

Back

False. A relation can have multiple outputs for a single input, which means it is not a function.

Front

Determine if the following is a function or relation: {(1, 4), (2, 5), (1, 5)}

Back

Relation. The input '1' has two different outputs (4 and 5).

Front

Determine if the following is a function or relation: {(0, 3), (1, 6), (2, 9), (3, 12)}

Back

Function. Each input has exactly one output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function. If a vertical line intersects the graph of the relation at more than one point, it is not a function.

Front

Identify the relation that is NOT a function: {(1,-5), (3,1), (-5,4), (4,-2)}, {(2,7), (3,7), (4,7), (5,8)}, {(1,-5), (-1,6), (1,5), (6,-3)}, {(3,-2), (5,-6), (7,7), (8,8)}

Back

{(1,-5), (-1,6), (1,5), (6,-3)}. The input '1' has two different outputs (-5 and 5).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system, where 'x' is the input and 'y' is the output.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.