Algebra Patterns & Functions Flashcards

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Questions and Answers

What is a sequence?

A collection of unordered numbers

A single number

An ordered list of numbers (correct)

A random list of numbers

What does recursive mean in mathematics?

A random pattern of numbers

A sequence of numbers not related to each other

The first number in a sequence

A consistent pattern in which each term relates to the previous term (correct)

What is an arithmetic sequence?

A sequence based on multiplication of terms

A sequence where the difference between any two consecutive terms is the same (correct)

A sequence that adds random numbers

A sequence of decimals only

What is common difference?

The difference between any two consecutive terms in an arithmetic sequence Signup and view all the answers

What defines a geometric sequence?

Each term is found by multiplying the previous term by the same number Signup and view all the answers

What is common ratio?

The nonzero number by which each term in a geometric sequence is multiplied Signup and view all the answers

What is a term in a sequence?

Each number in a sequence Signup and view all the answers

Define a function.

A relation in which each element of the domain is paired with exactly one element of the range Signup and view all the answers

What is the domain of a function?

The set of values of the independent variable for which a function is defined Signup and view all the answers

What is the range of a function?

The set of values of the dependent variable for which a function is defined Signup and view all the answers

What does one-to-one mapping refer to?

A mapping from set A to set B in which every member of B has exactly one preimage in A Signup and view all the answers

What is input in the context of functions?

The x-values (domain) of a relationship, or the value substituted into an expression or function Signup and view all the answers

What is output in a function?

The y-values (range) of a relationship, or the value resulting from substituting an input into a function Signup and view all the answers

Define an input-output table.

A chart of data where there is a collection of inputs and outputs that follow a specific rule Signup and view all the answers

What are ordered pairs?

Pairs of numbers (x, y) that can represent a point on the coordinate plane Signup and view all the answers

What is the vertical line test?

A test to determine if a graph is a function by checking if a vertical line intersects the graph at only one point Signup and view all the answers

What is function notation?

Notation that represents a function as f(x), g(x) or h(x) instead of y Signup and view all the answers

What is a coordinate plane?

A plane divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis Signup and view all the answers

What are quadrants in a coordinate plane?

Four regions into which a coordinate plane is divided by the x-axis and the y-axis Signup and view all the answers

Define a formula in mathematics.

An equation that shows a relationship between quantities represented by variables Signup and view all the answers

What is a rule in mathematics?

An equation or standard procedure for solving a class of mathematical problems Signup and view all the answers

What is function form?

A two or more variable equation written in function form if one variable is isolated on one side of the equation Signup and view all the answers

Study Notes

Sequences

A sequence is an ordered list of numbers, representing an arrangement where order matters.
Arithmetic Sequence features a consistent common difference between consecutive terms, indicating that the same number is added to each term.
A geometric sequence involves multiplication of the previous term by a fixed common ratio, creating a series based on multiplication rather than addition.

Recursion and Terms

The term recursive describes a pattern where each new term relates back to the term before it in a consistent way.
Each individual number within a sequence is called a term.

Functions

A function is a type of relation where every input (from the domain) is associated with exactly one output (from the range).
The domain consists of all possible input values for a function, while the range includes all possible output values resulting from those inputs.
One-to-one mapping ensures that every element of the output set corresponds to a unique element of the input set, avoiding multiple preimages.

Input and Output

Input refers to the x-values in a relation—values substituted into a function.
Output denotes the resulting y-values from an input, reflecting the value received after substitution in a function.
An input-output table organizes this relationship, displaying pairs of inputs and their corresponding outputs.

Graphical Representation

Ordered pairs represent points on a coordinate plane using x and y coordinates.
The vertical line test helps determine whether a graph represents a function; if a vertical line intersects the graph at only one point, it qualifies as a function.
The coordinate plane is divided into quadrants by the x-axis (horizontal) and y-axis (vertical), facilitating location identification of points.

Mathematical Representation

Function notation uses symbols like f(x), g(x), and h(x) to represent functions, distinguishing them from regular variables.
A formula succinctly expresses relationships between quantities represented by variables, serving as a foundational tool in algebra.
A rule outlines standard procedures or equations for solving specific types of mathematical problems, guiding approaches to problem-solving.

Function Form

A variable expressed in function form isolates one variable on one side of the equation, indicating how it functions as an output based on the input.

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Description

Explore essential concepts in algebra with these flashcards focusing on patterns and functions. Each card features key terms and their definitions, helping you to understand sequences, recursive patterns, and more. Perfect for reinforcing your knowledge in algebraic concepts.