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Complete a set of problems involving classification of functions, determining continuity, and converting between set builder and interval notation.

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By the end of this lesson, students will be able to determine the continuity of functions and classify functions as one-to-one and/or onto.

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Students will understand and apply: domain, codomain, range, one-to-one functions, onto functions, continuous functions, discrete functions, set builder notation, and interval notation.

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Students will develop skills in analyzing function graphs, determining continuity, and classifying functions based on their properties.

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Teacher-led presentation on domain, codomain, range, and the concepts of one-to-one and onto functions. Use visual aids and real-world examples to illustrate these concepts.

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Group activity: Students use Padlet to collaborate and share examples of continuous and discrete functions from everyday life. Discuss how to determine continuity from a graph.

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Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

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Practice converting between set builder and interval notation for various function domains and ranges. Students can use Padlet to post their solutions and peer review each other's work.

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Independent practice: Students analyze given functions and classify them as one-to-one, onto, both, or neither. They will also determine the continuity of these functions.

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Calculus I - Functions (Practice Problems)

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Here is a set of practice problems to accompany the Functions Section of the Review chapter of the notes for Paul Dawkins Calculus I course at Lamar University.

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Discuss how function properties are used in various fields such as economics (supply and demand curves), physics (motion graphs), and computer science (encryption functions).

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Real-World Applications of Functions: Calculus 1

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For advanced students: Explore the concept of inverse functions and how they relate to one-to-one functions. Investigate the graphical relationship between a function and its inverse.

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Inverse Functions – Understand in 10 Minutes

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For students needing additional support: Review basic function concepts and provide guided practice on identifying domain, codomain, and range using simpler examples.

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Learn Functions – Understand In 7 Minutes

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Throughout the lesson, use quick exit tickets to gauge understanding. Example: 'Give an example of a function that is one-to-one but not onto.'

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Students use Padlet to post their solutions to classification problems and provide feedback on their peers' work, promoting collaborative learning and self-assessment.

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End-of-lesson quiz covering all key concepts: continuity, one-to-one, onto, domain, range, and notation. Include both multiple-choice and short-answer questions.

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Properties of Functions | 82 plays | Quizizz

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Properties of Functions quiz for 9th grade students. Find other quizzes for Mathematics and more on Quizizz for free!

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In small groups, students create a concept map linking all the key terms and ideas from the lesson. They can use Padlet to collaboratively build and share their maps.

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Individual reflection: 1) What was the most challenging concept from today's lesson? 2) How do you think these function properties might be useful in a real-world context? 3) What questions do you still have about the material?

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Research a real-world scenario where function properties (continuity, one-to-one, onto) are important. Create a brief presentation explaining the application and its relevance to the concepts learned.

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Functions

Do you have a different outfit that you wear each day of the week? If so, you might be surprised to learn that the relationship between the day of the week and your outfit represents a mathematical concept called a function.

In mathematics, a function is a relationship between two sets of elements in which no element in the first set relates to more than one element in the second. We can think of a function as a rule that takes inputs from the first set and relates them to an element in the second set, which is the output.

In mathematics, we represent functions in many different ways; we can use words, tables, mappings, equations, and even graphs. Consider this example: If a state has a 6% sales tax, then we can use a function to calculate it. We can use the following equation to represent this function:

If we purchase a product for x dollars, then to calculate the tax, we would multiply x by 0.06, or the tax rate in decimal form. For instance, if you bought a shirt for $25, then you can calculate the sales tax by plugging in 25 for x.

T = 0.06(25) = 1.5

We see the sales tax is $1.50.

We can also represent this function using our other representations. Because our purchase price can be any number, we could never list all of the inputs and outputs! Using a table or mapping wouldn't be the best method in this situation, but we can easily represent it graphically by simply graphing the equation T = 0.06 x.

We see that there are many ways to represent a function, and each one depends on its context. Now that we are reminded what a function is in mathematics, let's talk some more about using them in real-world settings!

Functions in the Real World

When it comes to recognizing functions in the real world, it is useful to think of the term ''is a function of'' as ''is determined by.'' You see, in a function, no input can be related to two different outputs, otherwise, given the input, we couldn't determine the output. Therefore, the input determines the output, so the output is a function of the input.

For instance, think about those outfits again.

If it's Tuesday, what outfit will you be wearing? Well, we look to see what outfit to which Tuesday is mapped, and we see that you will be wearing your jean shorts with your green t-shirt. That's not too hard, is it? You can see that your outfit ''is determined by'' the day of the week, so your outfit ''is a function of'' the day of the week.

Pretty neat, huh? You may have been familiar with functions involving numbers, but it's totally cool to see that the function concept can actually be applied to real world situations! Let's consider a couple more examples!

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function application for the real world - video & lesson transcript | study.com

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Function Application for the Real World - Video & Lesson Transcript | Study.com

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Do you have a different outfit that you wear each day of the week? If so, you might be surprised to learn that the relationship between the day of the week and your outfit represents a mathematical concept called a function.

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Complete assigned exercises on an online platform to reinforce understanding of function properties and classification.

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Algebra has a reputation for being difficult, but Math Games makes struggling with it a thing of the past. Kids can use our free, exciting games to play and compete with their friends as they progress in this subject!

Algebra concepts that pupils can work on here include:

Solving and writing variable equations to find answers to real-world problems

Writing, simplifying and evaluating variable expressions to figure out patterns and rules

Solving linear equations and inequalities

Finding the slopes of graphs, and graphing proportional relationships and equations

Completing and writing rules for function tables

With Math Games, students can work at a suitable level for their individual abilities, in a format that's simple to use and lots of fun to engage with! They can also use our digital textbook, game applications or PDF worksheets. Choose a skill to start playing.

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math games practice algebra free math games practice common core standards

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Find Math games to practice every skill.