Algebra Unit 3 Flashcards

Functions and Relationships

• A function is a relationship where one quantity depends on another, indicating a dependent relationship.
• Function notation uses a letter (e.g., F) followed by parentheses containing the independent variable, pronounced as "F of x."

Domain and Range

• Domain refers to the complete set of allowable input values, represented by x-values on a graph.
• Range encompasses all output values (y-values) that a function can yield.

Inputs and Outputs

• Input is the independent variable that is entered into a function.
• Output is the dependent variable, resulting from the function's computation.

Input-Output Relationship

• Input-output diagrams illustrate the relationship between inputs and outputs using arrows to link them.
• Input-output tables organize inputs in one column and corresponding outputs in another.

Mappings and Relations

• Mapping connects inputs to outputs, with functional mappings requiring each input to be associated with a single output.
• A relation can map a single input to multiple outputs, differentiating it from a function.

Graphing and Lines

• Vertical lines run straight up and down; their equation is x = a.
• Horizontal lines run left to right, characterized by the equation y = a.
• The vertical line test determines if a graph is a function by checking for intersections with vertical lines.
• The horizontal line test assesses if a graph is a one-to-one function, meaning each output is paired with one unique input.

Function Types

• Many-to-one functions occur when multiple x-values correspond to a single y-value.
• One-to-one functions ensure that each output comes from only one input.

Sequences

• An arithmetic sequence features a consistent difference between consecutive terms.
• The common difference represents the fixed value between terms in an arithmetic sequence.
• A geometric sequence maintains a constant ratio between successive terms, termed common ratio.

Growth and Decay

• Exponential growth involves a quantity increasing by a consistent ratio over intervals.
• Exponential decay describes a quantity decreasing by a consistent ratio at regular intervals.

Mathematical Properties

• The commutative property states that the order of addition or multiplication doesn't affect the result: a + b = b + a and ab = ba.

Test your understanding of key terms in Algebra Unit 3 with these flashcards. Each card provides a definition for essential concepts such as functions, function notation, and domain. Perfect for students looking to reinforce their algebra skills.