Functions and Relations Quiz

Functions and Relations

• A function indicates a relationship where one quantity depends on another, establishing a dependent and independent variable connection.
• Function notation employs a letter designation for the function, using parentheses for the independent variable (e.g., F(x) pronounced "F of x").
• The domain consists of all permissible input values, represented by x-values in a function's graph.
• Input refers to the value entered into a function, represented as the independent variable.

Diagrams and Tables

• An input-output diagram visualizes the connection between inputs and outputs in a function.
• Output signifies the result produced by a function, considered the dependent variable.
• The range encompasses all output values that a function can produce (y-values).
• Mapping represents the structured connection of inputs to outputs; if each input links to only one output, it is classified as a function.
• A mapping diagram illustrates how specific relations pair input values with output values.
• An input-output table lists input values in the first column and corresponding output values in the second, representing domain and range.
• A table is a structured format for displaying data, organized in rows and columns for clarity.

Coordinate Geometry

• An ordered pair, defined in parentheses, indicates a point's location on a coordinate plane, comprising an x and y value.
• Vertical lines run straight up and down on a coordinate plane; their equation takes the form x = a, where 'a' is a constant.
• The vertical line test evaluates if a graph represents a function—if it intersects multiple points with a vertical line, it’s not a function.
• Horizontal lines extend from left to right in a coordinate plane, written as y = a, with 'a' as a constant.
• The horizontal line test checks if a graph is a one-to-one function.

Types of Functions

• A many-to-one function maps multiple x-values to a single y-value.
• A one-to-one function links each y-value to one unique x-value.

Sequences

• An arithmetic sequence maintains a constant difference between consecutive terms.
• The common difference refers to the fixed value separating consecutive numbers in an arithmetic sequence.
• A geometric sequence involves maintaining a consistent ratio between successive terms.
• The common ratio is the consistent multiplier between consecutive numbers in a geometric sequence.
• Exponential growth describes a quantity increasing by a common ratio at regular intervals, while exponential decay refers to a quantity decreasing in the same manner.
• A sequence presents an ordered pattern of numbers, exemplified by decreasing terms such as 11, 7, 3, -1, etc.

Properties of Operations

• The commutative property states that the order of addition or multiplication does not affect the result (e.g., a + b = b + a).