Remix of Indigenous Vocabulary: Algonquin Words

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Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.)

Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.). Sources: Sculptor: Peter Wolf Toth / Photo by: Niranjan Arminius - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=51375010

The Abenaki (Abnaki, Abinaki, Alnôbak) are a Native American tribe and First Nation. They are one of the Algonquian-speaking peoples of northeastern North America. The Abenaki originated in a region called Wabanahkik in the Eastern Algonquian languages (meaning "Dawn Land"), a territory now including parts of Quebec and the Maritimes of Canada and northern sections of the New England region of the United States. The Abenaki are one of the five members of the Wabanaki Confederacy.

The Abenaki language is closely related to the Panawahpskek (Penobscot) language. Other neighboring Wabanaki tribes, the Pestomuhkati (Passamaquoddy), Wolastoqiyik (Maliseet), and Miꞌkmaq, and other Eastern Algonquian languages share many linguistic similarities. It has come close to extinction as a spoken language. Tribal members are working to revive the Abenaki language at Odanak (means "in the village"), a First Nations Abenaki reserve near Pierreville, Quebec, and throughout New Hampshire, Vermont and New York state.

Twenty Basic Words in Algonquin

Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

Algonquin Word Set

English (Français) Algonquin Words
One (Un) Pejig
Two (Deux) Nìj
Three (Trois) Niswi
Four (Quatre) New
Five (Cinq) Nànan
Man (Homme) Ininì
Woman (Femme) Ikwe
Dog (Chien) Animosh
Sun (Soleil) Kìzis
Moon (Lune) Tibik-kìzis
Water (Eau) Nibì
White (Blanc) Wàbà
Yellow (Jaune) Ozàwà
Red (Rouge) Miskwà
Black (Noir) Makadewà
Eat (Manger) Mìdjin
See (Voir) Wàbi
Hear (Entendre) Nòndam
Sing (Chanter) Nigamo
Leave (Partir) Màdjà or Nagadàn

Test your memory

Please note: the content on this page, sourced from http://www.native-languages.org/algonquin_words.htm, is meant for demonstration purposes only.

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My Indigenous Vocabulary: Algonquin Words

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Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.)

Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.). Sources: Sculptor: Peter Wolf Toth / Photo by: Niranjan Arminius - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=51375010

The Abenaki (Abnaki, Abinaki, Alnôbak) are a Native American tribe and First Nation. They are one of the Algonquian-speaking peoples of northeastern North America. The Abenaki originated in a region called Wabanahkik in the Eastern Algonquian languages (meaning "Dawn Land"), a territory now including parts of Quebec and the Maritimes of Canada and northern sections of the New England region of the United States. The Abenaki are one of the five members of the Wabanaki Confederacy.

The Abenaki language is closely related to the Panawahpskek (Penobscot) language. Other neighboring Wabanaki tribes, the Pestomuhkati (Passamaquoddy), Wolastoqiyik (Maliseet), and Miꞌkmaq, and other Eastern Algonquian languages share many linguistic similarities. It has come close to extinction as a spoken language. Tribal members are working to revive the Abenaki language at Odanak (means "in the village"), a First Nations Abenaki reserve near Pierreville, Quebec, and throughout New Hampshire, Vermont and New York state.

Twenty Basic Words in Algonquin

Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

Algonquin Word Set

English (Français) Algonquin Words
One (Un) Pejig
Two (Deux) Nìj
Three (Trois) Niswi
Four (Quatre) New
Five (Cinq) Nànan
Man (Homme) Ininì
Woman (Femme) Ikwe
Dog (Chien) Animosh
Sun (Soleil) Kìzis
Moon (Lune) Tibik-kìzis
Water (Eau) Nibì
White (Blanc) Wàbà
Yellow (Jaune) Ozàwà
Red (Rouge) Miskwà
Black (Noir) Makadewà
Eat (Manger) Mìdjin
See (Voir) Wàbi
Hear (Entendre) Nòndam
Sing (Chanter) Nigamo
Leave (Partir) Màdjà or Nagadàn

Test your memory

Please note: the content on this page, sourced from http://www.native-languages.org/algonquin_words.htm, is meant for demonstration purposes only.

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Remix of Functions and Function Notation

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Learning Objectives

In this section, you will:

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the domain and the set consisting of the second components of each ordered pair is called the range. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).

Note that each value in the domain is also known as an input value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable, and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no x-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).

Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as

$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$

Notice that each element in the domain, \(\{even, odd\}\) is not paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.

Figure 1 compares relations that are functions and not functions.

Three relations that demonstrate what constitute a function.

Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.

Functions

function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”

The input values make up the domain, and the output values make up the range.

Examples

Given a relationship between two quantities, determine whether the relationship is a function.

Using Function Notation

Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.

To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.

$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$

Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add a and b, and the result is the input for the function f." The operations must be performed in this order to obtain the correct result.

Function Notation

The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.

Practice Quiz

Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites

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1.1 Accounting: The Language of Business

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Understanding the Role of Accounting

Accounting is an information system that measures and records business activities. The role of accounting is to identify, record, and measure the transactions or activities in a business to be able to evaluate its performance and assess its financial health

- (Harrison et al., 2018, p. 3)

This information is communicated to stakeholders using financial statements that contain useful information to help them make rational economic decisions. Financial statements are prepared based on a set of accounting rules, such as Generally Accepted Accounting Principles (GAAP) or International Financial Reporting Standards (IFRS); these help standardize accounting across businesses. Review the flow of accounting information diagram below.  

Graphic illustration displaying the 3 steps of the flow of information in accounting

The Flow of Accounting Information. People make decisions, business transactions occur, companies report their results. The process is cyclical.

This diagram illustrates the flow of accounting information and helps illustrate accounting’s role in business. The accounting process begins and ends with people making decisions.

Let’s apply the flow of accounting information to a real business: Apple Inc.

In this diagram, it begins with production. Apple Inc. produces a new annual line up of its iPhone. Then, it moves to purchasing. Customers make purchases at the store. From there is reporting. Revenues from the product and expenses from operating the store are reported in Apple’s quarterly and annual reports. These financial results inform managers’ decisions regarding product line, stocking, etc. This brings us back to production.

The Four Financial Statements

The flow of accounting results in transactions that are recorded and presented using four important financial statements to report the results to various stakeholders. We will explore these four financial statements further in the next topic.

Note: The order is important! The first is income statements, then statement of retained earnings, balance sheet, and lastly statement of cash flow. 

Users of Financial Information

These financial statements are used by different stakeholders. So, who are the users of financial information?

Managers: set goals, evaluate those goals, and take corrective action.

  • Most companies hire managers to oversee the day-to-day operations of the business (i.e., operating activities).

  • Managers make many business decisions using accounting info:

    • Should they build a new product line?
    • Should they open a regional sales office?
    • Should they acquire a competitor?
    • Should they extend credit to their major customers?

Investors: decide whether to invest in a business or evaluate an investment.

  • Investors are individuals/groups who provide capital to finance a business’s activities by purchasing ownership interest. They own shares of the business and are called shareholders.

  • Investors look for two sources of possible gain:

    • Sell ownership interest in the future for more than they paid.
    • Receive a portion of the company’s earnings in cash (dividends).
  • Investors (shareholders) use accounting information to find out how much income they can expect to earn on their investment and where to invest their money.

  • You too are an investor if you buy stocks, debt, or real estate! Financial information can help you decide where to invest your money.

Creditors: evaluate a borrower’s ability to make required payments.

  • Creditors provide capital to finance a business’s activities by lending money. Unlike investors, creditors do not own a share of the company.

  • For example, a bank lends funds to a company in the form of a loan that must be repaid by the company in the future along with interest.

Image 3

Banks loan companies funds, but must be repaid with interest.

Government and regulatory bodies such as Canada Revenue Agency (CRA): ensure organizations pay the correct amount of taxes.

  • Government and regulatory bodies use accounting information for taxation and regulation of the stock markets. 

  • For example, the CRA uses financial information to compute the sales and business taxes owed by a business and the Ontario Securities Commission requires periodic financial information from companies that are stock listed on the Toronto Stock Exchange (TSX).

Individuals: make investment decisions and/or manage a bank account.

  • Individuals like you and me use financial information to make daily purchasing decisions.

  • Do you budget your annual, monthly, or weekly spending? Even high-level budgeting of your tuition, rent, food, and transportation is, in a way, using financial information to determine your financial needs.

Not-for-profit organizations: use accounting information in virtually the same way as for-profit organizations.

  • Like for-profit companies, not-for-profit organizations use financial information to make decisions about their operations and investments, and to report financial information to their users.

  • Users of financial information for a not-for-profit organization include board members, managers, and the CRA.

  • The CRA has a designated non-taxable business status for approved not-for-profit organizations. These designated organizations need to comply with reporting requirements and do not have to pay regular business taxes like for-profit companies.

Financial vs. Management Accounting

Since different users have different reporting needs and underlying reasons for financial information, there are two types of accounting information:

Financial Accounting

Financial accounting provides information for different internal and external users:

  • Internal users
    • Managers

    • Investors

  • External users
    • Creditors

    • Government

    • Public

Financial accounting is the focus of our course!

Management Accounting

Management accounting provides the following information for internal users only:

  • Budgets

  • Forecasts

  • Projections

  • Detailed product level/department level information

This is most likely your next accounting course!

Types of Business Organizations

There are three main forms of business organizations: proprietorship, partnership, and corporation.

 

  Proprietorship Partnership Corporation
Owner(s) Single owner known as the proprietor Generally two or more partners are co-owners

Owned by shareholders and legally formed under federal or provincial law:

  • Public company: many shareholders (i.e. Apple)

  • Private company: small number of shareholders (i.e. a small business)

Personal liability of owner(s) for business debts Proprietor is personally liable Partners are usually personally liable Shareholders are not personally liable
Life of entity Limited by owner’s choice or death Limited by owner’s choice or death Indefinite (owned by shareholders)
Tax structure Included in personal taxes of the proprietor Doesn’t pay taxes as income flows through to individual partners and is taxed at their personal tax rate Corporation pays taxes and any dividends paid to shareholders are taxed at their personal tax rate
Examples

Common business structure for self-employed, small retail stores, or professional service providers:

  • Lawyers

  • Accountants

The Big Four accounting companies are all partnerships:

  • PwC LLP

  • KPMG LLP

  • Deloitte LLP
  • EY LLP

Public companies:

  • Apple Inc.
  • Alphabet Inc.
  • Amazon Inc.
  • Wal-Mart Inc.

Private companies:

  • IKEA
  • Koch Industries
  • Bechtel
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Example of a Lesson

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COURSE101

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Quick Quiz

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Vivamus suscipit tortor eget felis porttitor volutpat. Vivamus suscipit tortor eget felis porttitor volutpat. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Donec velit neque, auctor sit amet aliquam vel, ullamcorper sit amet ligula. Donec sollicitudin molestie malesuada.

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Vivamus suscipit tortor eget felis porttitor volutpat. Pellentesque in ipsum id orci porta dapibus. Donec sollicitudin molestie malesuada. Donec rutrum congue leo eget malesuada.

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MAT1L Lesson Template

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Learning Objectives

  1. Add learning objectives here
  2. Examples of learning objectives can include:
  3. Understand how to solve for 'x'
  4. Read and create functions
  5. And so on
Photo of a pen on top of paper with math expressions

Swap out this image with an image of your own.

Introduction to the Lesson should go here. You should introduce the topic in one or two paragraphs. 

Praesent nonummy mi in odio. Phasellus magna. In dui magna, posuere eget, vestibulum et, tempor auctor, justo. Nulla neque dolor, sagittis eget, iaculis quis, molestie non, velit.

You can also add mathematical expressions and functions using the LaTex notation. For example the following syntax:

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

Produces the following expression:

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

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Remix of Functions and Function Notation

Content Blocks

Learning Objectives

In this section, you will:

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the domain and the set consisting of the second components of each ordered pair is called the range. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).

Note that each value in the domain is also known as an input value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable, and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no x-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).

Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as

$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$

Notice that each element in the domain, \(\{even, odd\}\) is not paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.

Figure 1 compares relations that are functions and not functions.

Three relations that demonstrate what constitute a function.

Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.

Functions

function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”

The input values make up the domain, and the output values make up the range.

Examples

Given a relationship between two quantities, determine whether the relationship is a function.

Using Function Notation

Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.

To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.

$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$

Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add a and b, and the result is the input for the function f." The operations must be performed in this order to obtain the correct result.

Function Notation

The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.

Practice Quiz

Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites

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Daring Dragon - Remix of Indigenous Vocabulary: Algonquin Words

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Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.)

Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.). Sources: Sculptor: Peter Wolf Toth / Photo by: Niranjan Arminius - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=51375010

The Abenaki (Abnaki, Abinaki, Alnôbak) are a Native American tribe and First Nation. They are one of the Algonquian-speaking peoples of northeastern North America. The Abenaki originated in a region called Wabanahkik in the Eastern Algonquian languages (meaning "Dawn Land"), a territory now including parts of Quebec and the Maritimes of Canada and northern sections of the New England region of the United States. The Abenaki are one of the five members of the Wabanaki Confederacy.

The Abenaki language is closely related to the Panawahpskek (Penobscot) language. Other neighboring Wabanaki tribes, the Pestomuhkati (Passamaquoddy), Wolastoqiyik (Maliseet), and Miꞌkmaq, and other Eastern Algonquian languages share many linguistic similarities. It has come close to extinction as a spoken language. Tribal members are working to revive the Abenaki language at Odanak (means "in the village"), a First Nations Abenaki reserve near Pierreville, Quebec, and throughout New Hampshire, Vermont and New York state.

Twenty Basic Words in Algonquin

Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

Algonquin Word Set

English (Français) Algonquin Words
One (Un) Pejig
Two (Deux) Nìj
Three (Trois) Niswi
Four (Quatre) New
Five (Cinq) Nànan
Man (Homme) Ininì
Woman (Femme) Ikwe
Dog (Chien) Animosh
Sun (Soleil) Kìzis
Moon (Lune) Tibik-kìzis
Water (Eau) Nibì
White (Blanc) Wàbà
Yellow (Jaune) Ozàwà
Red (Rouge) Miskwà
Black (Noir) Makadewà
Eat (Manger) Mìdjin
See (Voir) Wàbi
Hear (Entendre) Nòndam
Sing (Chanter) Nigamo
Leave (Partir) Màdjà or Nagadàn

Test your memory

Please note: the content on this page, sourced from http://www.native-languages.org/algonquin_words.htm, is meant for demonstration purposes only.

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Remix (Test) of Indigenous Vocabulary: Algonquin Words

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Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.)

Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.). Sources: Sculptor: Peter Wolf Toth / Photo by: Niranjan Arminius - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=51375010

The Abenaki (Abnaki, Abinaki, Alnôbak) are a Native American tribe and First Nation. They are one of the Algonquian-speaking peoples of northeastern North America. The Abenaki originated in a region called Wabanahkik in the Eastern Algonquian languages (meaning "Dawn Land"), a territory now including parts of Quebec and the Maritimes of Canada and northern sections of the New England region of the United States. The Abenaki are one of the five members of the Wabanaki Confederacy.

The Abenaki language is closely related to the Panawahpskek (Penobscot) language. Other neighboring Wabanaki tribes, the Pestomuhkati (Passamaquoddy), Wolastoqiyik (Maliseet), and Miꞌkmaq, and other Eastern Algonquian languages share many linguistic similarities. It has come close to extinction as a spoken language. Tribal members are working to revive the Abenaki language at Odanak (means "in the village"), a First Nations Abenaki reserve near Pierreville, Quebec, and throughout New Hampshire, Vermont and New York state.

Twenty Basic Words in Algonquin

Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

Algonquin Word Set

English (Français) Algonquin Words
One (Un) Pejig
Two (Deux) Nìj
Three (Trois) Niswi
Four (Quatre) New
Five (Cinq) Nànan
Man (Homme) Ininì
Woman (Femme) Ikwe
Dog (Chien) Animosh
Sun (Soleil) Kìzis
Moon (Lune) Tibik-kìzis
Water (Eau) Nibì
White (Blanc) Wàbà
Yellow (Jaune) Ozàwà
Red (Rouge) Miskwà
Black (Noir) Makadewà
Eat (Manger) Mìdjin
See (Voir) Wàbi
Hear (Entendre) Nòndam
Sing (Chanter) Nigamo
Leave (Partir) Màdjà or Nagadàn

Please note: the content on this page, sourced from http://www.native-languages.org/algonquin_words.htm, is meant for demonstration purposes only.

Test your memory

Assessment

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Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

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My Remix of Functions and Function Notation

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Learning Objectives

In this section, you will:

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the domain and the set consisting of the second components of each ordered pair is called the range. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).

Note that each value in the domain is also known as an input value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable, and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no x-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).

Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as

$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$

Notice that each element in the domain, \(\{even, odd\}\) is not paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.

Figure 1 compares relations that are functions and not functions.

Three relations that demonstrate what constitute a function.

Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.

Functions

function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”

The input values make up the domain, and the output values make up the range.

Examples

Given a relationship between two quantities, determine whether the relationship is a function.

Using Function Notation

Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.

To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.

$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$

Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add a and b, and the result is the input for the function f." The operations must be performed in this order to obtain the correct result.

Function Notation

The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.

Practice Quiz

Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites

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A demonstration of the MathJax authoring capabilities. Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites

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