Functions and Relations Quiz

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Questions and Answers

What is a function?

A special type of relationship in algebra where two quantities are related to each other so that one quantity depends on the other.

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 in a function?

The set of all allowable input values.

What is an input?

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

What is an input-output diagram?

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

What is output in 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 refer to in 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?

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

What is an input-output table?

<p>A two-column table with input values in the first column and output values in the second column.</p> Signup and view all the answers

What is a table in the context of functions?

<p>A useful tool for recording data about functions.</p> Signup and view all the answers

What is an ordered pair?

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

What does vertical mean in a coordinate plane?

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

What is the vertical line test?

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

What does horizontal mean in a coordinate plane?

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

What is the horizontal line test?

<p>A method for testing whether 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 in which each y-value has a single x-value mapped to it.</p> Signup and view all the answers

What is an arithmetic sequence?

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

What is a common difference?

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

What is a common ratio?

<p>The constant ratio between any 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 where 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 addition or multiplication of two numbers in either order will not change the answer.</p> Signup and view all the answers

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Study Notes

Functions and Relations

  • A function indicates a relationship where one quantity depends on another, establishing a dependent and independent variable connection.
  • Function notation employs a letter designation for the function, using parentheses for the independent variable (e.g., F(x) pronounced "F of x").
  • The domain consists of all permissible input values, represented by x-values in a function's graph.
  • Input refers to the value entered into a function, represented as the independent variable.

Diagrams and Tables

  • An input-output diagram visualizes the connection between inputs and outputs in a function.
  • Output signifies the result produced by a function, considered the dependent variable.
  • The range encompasses all output values that a function can produce (y-values).
  • Mapping represents the structured connection of inputs to outputs; if each input links to only one output, it is classified as a function.
  • A mapping diagram illustrates how specific relations pair input values with output values.
  • An input-output table lists input values in the first column and corresponding output values in the second, representing domain and range.
  • A table is a structured format for displaying data, organized in rows and columns for clarity.

Coordinate Geometry

  • An ordered pair, defined in parentheses, indicates a point's location on a coordinate plane, comprising an x and y value.
  • Vertical lines run straight up and down on a coordinate plane; their equation takes the form x = a, where 'a' is a constant.
  • The vertical line test evaluates if a graph represents a function—if it intersects multiple points with a vertical line, it’s not a function.
  • Horizontal lines extend from left to right in a coordinate plane, written as y = a, with 'a' as a constant.
  • The horizontal line test checks if a graph is a one-to-one function.

Types of Functions

  • A many-to-one function maps multiple x-values to a single y-value.
  • A one-to-one function links each y-value to one unique x-value.

Sequences

  • An arithmetic sequence maintains a constant difference between consecutive terms.
  • The common difference refers to the fixed value separating consecutive numbers in an arithmetic sequence.
  • A geometric sequence involves maintaining a consistent ratio between successive terms.
  • The common ratio is the consistent multiplier between consecutive numbers in a geometric sequence.
  • Exponential growth describes a quantity increasing by a common ratio at regular intervals, while exponential decay refers to a quantity decreasing in the same manner.
  • A sequence presents an ordered pattern of numbers, exemplified by decreasing terms such as 11, 7, 3, -1, etc.

Properties of Operations

  • The commutative property states that the order of addition or multiplication does not affect the result (e.g., a + b = b + a).

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