Functions and Relations Quiz

Domain and Functions

• Domain: Refers to the x-values (inputs) of a relation or function.
• Function: A specific type of relation where each x-value correlates with one unique y-value, meaning no repetition of x-values occurs in ordered pairs.

Input and Output

• Input: Represents the x-value in a relation or function.
• Output: Represents the y-value in a relation or function.

Range and Relation

• Range: Consists of the y-values (outputs) of a relation or function.
• Relation: Any set of numbers represented on a coordinate plane (x, y) that can sometimes be a function but isn't necessarily one.

Concept of a Function

• A function mandates that each input yields only one output, reflecting real-world restrictions, like a person’s weight being singular at any given time.
• An example of a function includes paired elements like (0, 2), (4, 9), (6, 12), and (7, 2), where each x-value has a single corresponding y-value.

Identifying Functions

• Situations where multiple inputs produce the same output (like a car starting and ending at the same position) still qualify as functions if each input leads to a singular output.
• Non-functional examples arise when a single input corresponds to multiple outputs, illustrated by pairs like (0, 2), (4, 9), (5, 6), (5, 8), showing that 5 produces two different outputs.

Graphical Representation

• Graphs of two-variable equations consist of points represented as ordered pairs, forming a relation.
• For infinite ordered pairs, the relation is best expressed through the rule method or the equation itself, while finite sets work well with the list method.

Example Relations

• Example 1: Set A = {(6, 2), (2, 6), (4, 1), (4, 0)} is a relation since it contains ordered pairs. However, it is not a function due to repetitive x-values (4 appears twice).