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Students will be able to find the domain of rational functions by identifying values that make the denominator equal to zero and expressing the domain using interval notation.

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This lesson aligns with A-APR.D.6: Rewrite simple rational expressions in different forms and F-IF.A.1: Understand that a function from one set to another assigns exactly one output to each input.

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Why are certain values excluded from the domain of rational functions, and how do we identify these restrictions?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined. For rational functions, we must exclude values that make the denominator zero.

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How To Find The Domain of a Function - Radicals, Fractions & Square Roots - Interval Notation

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A rational function has the form f(x) = P(x)/Q(x) where P(x) and Q(x) are polynomials and Q(x) ≠ 0. To find the domain, set the denominator equal to zero and solve for x. These x-values are excluded from the domain.

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1. Identify the denominator Q(x)
2. Set Q(x) = 0
3. Solve for x
4. Exclude these x-values from the domain
5. Express domain in interval notation or set notation

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Find the domain of f(x) = (x+3)/(x-2). Set denominator equal to zero: x-2 = 0, so x = 2. Domain: (-∞, 2) ∪ (2, ∞) or all real numbers except x = 2.

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Work in pairs to find domains of various rational functions. Use Padlet to share your solutions and explain your reasoning. Each pair posts one worked example with clear steps shown.

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Practice finding domains of rational functions with linear denominators. Complete problems 1-8 on the provided worksheet focusing on single restrictions.

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Advanced students: Find domains of rational functions with higher degree polynomials in denominators. Explore functions with multiple restrictions and complex factoring.

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Students needing extra support: Review polynomial factoring and solving equations. Use visual number line representations to understand domain restrictions.

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Factoring Trinomials & Polynomials, Basic Introduction - Algebra

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Quick check: Find the domain of h(x) = (x-1)/(x²-9). Students write their answer and briefly explain their process before leaving class.

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During guided practice, observe students' ability to: identify denominators, set up equations, solve for restrictions, and express domains correctly in interval notation.

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Students check each other's work during collaborative activities, providing feedback on accuracy of domain identification and mathematical notation.

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Tomorrow's quiz will include 5 problems requiring students to find domains of rational functions with various types of denominators and express answers in proper notation.

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Domain Rational Functions 11th - 12th Grade Quiz | Wayground (formerly Quizizz)

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Domain Rational Functions quiz for 11th grade students. Find other quizzes for Mathematics and more on Wayground for free!

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Think about today's lesson, pair up with a classmate, and share: What is the key to finding the domain of any rational function? How is this different from other types of functions?

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Before leaving, write down: 3 things you learned about domains, 2 questions you still have, and 1 way you'll remember to find domain restrictions.

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Today we learned that rational function domains exclude values that make denominators zero. We practiced identifying these restrictions and expressing domains using interval notation.

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Complete the 'Finding Domains of Rational Functions' worksheet with 15 problems of varying difficulty. Show all work and express final answers in interval notation.

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Play the interactive domain-finding game for 20 minutes. Focus on rational functions and track your progress. Screenshot your final score for tomorrow's class.

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Continuous Everywhere but Differentiable Nowhere

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TL;DR: An interactive activity having kids ask each other questions to guess the rational function graph they have on their foreheads. *** I’m going to make a short post inspired by Twitter M…

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Research and find one real-world example where rational functions are used. Identify what the domain restrictions might represent in that context. Write a short paragraph explanation.

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Review today's notes and be ready to discuss any questions. Tomorrow we'll explore graphing rational functions and how domain restrictions appear visually.

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What so special about the domain of a rational function?