# Math Mondays: Polynomials in PreCalculus - Graphing Rational Functions

We started Unit 2: Polynomials in PreCalculus. Quadratic functions go fast, as this is the third time they have seen them. I would like to say that I get super creative for Quadratic Functions. I would, but I don't. We fly through them focusing on factoring, solving, and graphing. I spend more time in this unit on the concepts which I find can be challenging - zeros of polynomial functions, polynomial division, and graphing rational functions.

Graphing rational functions is often difficult. I get it. The process is not instinctual to me. I am more likely to rely on a graphing calculator, and my students would love to just use theirs. We do work with calculators, but first students need to understand what that calculator is doing.

A couple of years back, I developed color-coded graphic organizers for graphing rational functions. The different colors help students visualize each step. So part one is to have students complete their graphic organizers. We review finding the intercepts and asymptotes and what is meant by neighborhoods. Coolmath.com has an excellent explanation of how to graph rational functions which students can use in completing their graphic organizers. We do some practice problems together and more individually.

This is a partner (or small group) activity that involves putting together puzzles. Each puzzle has four parts: an equation, a graph, the intercepts and the asymptotes. Students find the parts that go together for the same equation. For an added challenge, there are 3 blank puzzle pieces. Students determine which piece is missing and then find the correct solution for that piece and write the solution on the piece to complete the puzzle. I love that this activity is self-checking and also challenging in finding the missing information. (HINT: To get students moving, place puzzle pieces at 4 different stations. Each group has its own color of paper to find pieces at. Students get no more than four puzzle pieces at a time, so that they need to get up and go back to help find solutions).

Stay tuned for real-world logarithms in the next Pre-Calculus installment of Math Mondays.

PreCalculus Day 1

Functions and Graphs

Polynomials

Exponents and Logarithms

Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Matrices

Analytic Geometry in 2 and 3 dimensions

Discrete Mathematics

Introducing Limits - the Calculus of PreCalculus

Graphing rational functions is often difficult. I get it. The process is not instinctual to me. I am more likely to rely on a graphing calculator, and my students would love to just use theirs. We do work with calculators, but first students need to understand what that calculator is doing.

**Part one: Notes with coolmath.**A couple of years back, I developed color-coded graphic organizers for graphing rational functions. The different colors help students visualize each step. So part one is to have students complete their graphic organizers. We review finding the intercepts and asymptotes and what is meant by neighborhoods. Coolmath.com has an excellent explanation of how to graph rational functions which students can use in completing their graphic organizers. We do some practice problems together and more individually.

**Part two: It's a puzzle.**This is a partner (or small group) activity that involves putting together puzzles. Each puzzle has four parts: an equation, a graph, the intercepts and the asymptotes. Students find the parts that go together for the same equation. For an added challenge, there are 3 blank puzzle pieces. Students determine which piece is missing and then find the correct solution for that piece and write the solution on the piece to complete the puzzle. I love that this activity is self-checking and also challenging in finding the missing information. (HINT: To get students moving, place puzzle pieces at 4 different stations. Each group has its own color of paper to find pieces at. Students get no more than four puzzle pieces at a time, so that they need to get up and go back to help find solutions).

Stay tuned for real-world logarithms in the next Pre-Calculus installment of Math Mondays.

*This is part of a series of posts focused on***teaching PreCalculus**. Topics include:PreCalculus Day 1

Functions and Graphs

Polynomials

Exponents and Logarithms

Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Matrices

Analytic Geometry in 2 and 3 dimensions

Discrete Mathematics

Introducing Limits - the Calculus of PreCalculus

*Math Mondays is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math. If you have questions or think there is something I should include, you can leave me a message in the comments section below or at*

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