Functions vs Relations

The video tutorial introduces a problem about relations and functions, asking which statement is always true. It explains the concepts of relations and functions, highlighting that every function is a relation but not every relation is a function. The vertical line test is used to determine if a relation is a function. The correct answer is identified as 'every function is a relation'.

Which statement is always true about functions and relations?

• Every function is a relation.

• A function is not a relation.

• Every relation is a function.

• A relation is not a function.

What is a relation in mathematical terms?

• A rule that assigns multiple outputs to one input.

• Any relationship between two numbers.

• A set of numbers with no connection.

• A specific type of function.

Which of the following is a characteristic of a function?

• Each input has exactly one output.

• Each input can have multiple outputs.

• Inputs and outputs are unrelated.

• Functions are not related to relations.

What test can be used to determine if a relation is a function?

• Horizontal line test.

• Diagonal line test.

• Vertical line test.

• Circular line test.

Why does the pair (-2, 5) and (-2, -5) not represent a function?

• Because they are the same point.

• Because they are not related.

• Because they pass the vertical line test.

• Because they fail the vertical line test.