Algebra Unit 3 Flashcards

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Questions and Answers

What is a function?

A relationship where quantities depend on each other (correct)

A random set of numbers

A constant value

A single number

What is function notation?

A type of writing that uses a letter to name a function and places parentheses around the independent variable.

What is the domain of a function?

The set of all allowable input values.

What is an input in the context of a function?

A number that is entered into a function. Signup and view all the answers

What does an input-output diagram show?

It relates the inputs of a function to its outputs. Signup and view all the answers

What is the output of a function?

The result of a function. Signup and view all the answers

What is the range of a function?

The set of a function's output values. Signup and view all the answers

What does mapping mean in the context of functions?

A specified way of connecting inputs to outputs. Signup and view all the answers

What is a mapping diagram?

A diagram that shows how a specific relation maps input values to output values. Signup and view all the answers

What is a relation in mathematics?

Any set of input and output values. Signup and view all the answers

What does an input-output table display?

A two-column table of input and output values. Signup and view all the answers

What is an ordered pair?

A pair of numbers in parentheses indicating a point on a coordinate plane. Signup and view all the answers

What does vertical mean in geometry?

Straight up and down. Signup and view all the answers

What is the vertical line test?

A method for testing if a graph represents a function. Signup and view all the answers

What does horizontal mean in geometry?

Straight from left to right. Signup and view all the answers

What is the horizontal line test?

A method for testing if a graph is a one-to-one function. Signup and view all the answers

What is a many-to-one function?

A function in which two or more x-values map to a given y-value. Signup and view all the answers

What is a one-to-one function?

A function where each input maps to a unique output. Signup and view all the answers

What is an arithmetic sequence?

A sequence of numbers with the same difference between consecutive terms. Signup and view all the answers

What is common difference?

The constant value between two consecutive numbers in an arithmetic sequence. Signup and view all the answers

What is common ratio?

The constant ratio between two consecutive numbers in a geometric sequence. Signup and view all the answers

What is exponential decay?

A situation where a quantity decreases by a common ratio at regular intervals. Signup and view all the answers

What is exponential growth?

A situation where a quantity increases by a common ratio at regular intervals. Signup and view all the answers

What is a geometric sequence?

A sequence of numbers in which the ratio of any two successive terms is equal. Signup and view all the answers

What is a sequence?

An ordered pattern of numbers. Signup and view all the answers

What is the commutative property?

A rule stating that adding or multiplying two numbers in either order will not change the answer. Signup and view all the answers

Study Notes

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.

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Description

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.