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?

<p>A number that is entered into a function.</p> Signup and view all the answers

What does an input-output diagram show?

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

What is the output of a function?

<p>The result of a function.</p> Signup and view all the answers

What is the range of a function?

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

What does mapping mean in the context of functions?

<p>A specified way of connecting inputs to outputs.</p> Signup and view all the answers

What is a mapping diagram?

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

What is a relation in mathematics?

<p>Any set of input and output values.</p> Signup and view all the answers

What does an input-output table display?

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

What is an ordered pair?

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

What does vertical mean in geometry?

<p>Straight up and down.</p> Signup and view all the answers

What is the vertical line test?

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

What does horizontal mean in geometry?

<p>Straight from left to right.</p> Signup and view all the answers

What is the horizontal line test?

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

What is a many-to-one function?

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

What is a one-to-one function?

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

What is an arithmetic sequence?

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

What is common difference?

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

What is common ratio?

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

What is exponential decay?

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

What is exponential growth?

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

What is a geometric sequence?

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

What is a sequence?

<p>An ordered pattern of numbers.</p> Signup and view all the answers

What is the commutative property?

<p>A rule stating that adding or multiplying two numbers in either order will not change the answer.</p> 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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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.

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