Questions and Answers
What is an arithmetic sequence?
What is the common difference in an arithmetic sequence?
The difference between consecutive terms
Which of the following describes a continuous graph?
What is a dependent variable?
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What characterizes a discrete graph?
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What is the domain in mathematics?
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Define a function.
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What is function notation?
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What is an independent variable?
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What does input refer to in a function?
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What is a linear function?
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Define a nonlinear function.
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What does output refer to in a function?
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What is the range in mathematics?
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Define a relation.
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What is a sequence?
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What is a term of a sequence?
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What is the vertical line test used for?
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Study Notes
Key Concepts in Algebra
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Arithmetic Sequence: A sequence formed by adding a constant value (common difference) to each previous term to generate the next term.
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Common Difference: The fixed difference between consecutive terms in an arithmetic sequence, essential for determining the next term in the sequence.
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Continuous Graph: A type of graph that remains unbroken, representing smooth transitions between points.
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Dependent Variable: Represents the output values in a function; its value is dependent on the input provided by the independent variable.
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Discrete Graph: Composed of isolated points, contrasting with continuous graphs; often represents data that are not connected.
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Domain: The complete set of possible input values (independent variable values) for a relation or function, crucial for understanding restrictions on inputs.
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Function: Defines a relation that assigns exactly one output (dependent variable) for each input (independent variable), ensuring a unique mapping.
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Function Notation: Standard way to express functions, typically in the format f(x) instead of using Y; simplifies communication of functions.
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Independent Variable: The input variable of a function that determines the output value; its changes directly affect the dependent variable.
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Input: Refers to the specific value of the independent variable fed into a function to produce an output.
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Linear Function: A particular type of function whose graph yields a straight line; characterized by a constant rate of change.
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Nonlinear Function: A function whose graph is not a straight line, displaying varying rates of change; often includes quadratics, exponentials, etc.
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Output: The value produced by the function for a given input; corresponds to the dependent variable.
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Range: Represents the set of all possible output values for a relation, providing insights into the function's behavior.
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Relation: Refers to any collection of ordered pairs; can represent various relationships between quantities.
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Sequence: An ordered list of numbers often following a specific pattern, integral for understanding progression in mathematics.
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Term of Sequence: Any individual number within a sequence, contributing to the overall pattern.
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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.
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Description
Test your knowledge with these flashcards covering key concepts from Algebra 1 Unit 5. Topics include arithmetic sequences, common differences, continuous graphs, and dependent variables. Great for reviewing before your test!
