Algebra 1 Unit 5 Test Flashcards

Study Notes

Key Concepts in Algebra

Arithmetic Sequence: A sequence formed by adding a constant value (common difference) to each previous term to generate the next term.
Common Difference: The fixed difference between consecutive terms in an arithmetic sequence, essential for determining the next term in the sequence.
Continuous Graph: A type of graph that remains unbroken, representing smooth transitions between points.
Dependent Variable: Represents the output values in a function; its value is dependent on the input provided by the independent variable.
Discrete Graph: Composed of isolated points, contrasting with continuous graphs; often represents data that are not connected.
Domain: The complete set of possible input values (independent variable values) for a relation or function, crucial for understanding restrictions on inputs.
Function: Defines a relation that assigns exactly one output (dependent variable) for each input (independent variable), ensuring a unique mapping.
Function Notation: Standard way to express functions, typically in the format f(x) instead of using Y; simplifies communication of functions.
Independent Variable: The input variable of a function that determines the output value; its changes directly affect the dependent variable.
Input: Refers to the specific value of the independent variable fed into a function to produce an output.
Linear Function: A particular type of function whose graph yields a straight line; characterized by a constant rate of change.
Nonlinear Function: A function whose graph is not a straight line, displaying varying rates of change; often includes quadratics, exponentials, etc.
Output: The value produced by the function for a given input; corresponds to the dependent variable.
Range: Represents the set of all possible output values for a relation, providing insights into the function's behavior.
Relation: Refers to any collection of ordered pairs; can represent various relationships between quantities.
Sequence: An ordered list of numbers often following a specific pattern, integral for understanding progression in mathematics.
Term of Sequence: Any individual number within a sequence, contributing to the overall pattern.
Vertical Line Test: A technique utilized to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, the relation is not a function.