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

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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Description

Test your understanding of functions and relations with this quiz. Dive into concepts such as dependent and independent variables, function notation, domain, and range. Prepare to visualize these connections through diagrams and mappings.

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