Algebra 2 Lesson

Holes, Asymptotes & End Behavior: Analyzing Rational Functions

Shared by A STEM Educator

11th GradeBTC Style / Thinking Classrooms50 min

Learning Objective

Students will analyze rational functions by identifying domain restrictions, classifying discontinuities as removable holes or vertical asymptotes using numeric tables, and determining horizontal or slant asymptotes through polynomial division and end-behavior reasoning.

Lesson Overview

Students progress from identifying domain restrictions via factoring, through numeric table analysis to distinguish holes from vertical asymptotes, to determining horizontal and slant asymptotes using end-behavior ratios and polynomial division.

Materials

Vertical whiteboards or large sections of board space
Dry-erase markers (multiple colors)
Pencil and paper for numeric tables
Basic calculator (phone calculator is fine)

Scaffolded Task Progression

1Task 1

Find the domain of

f (x) = \frac{x + 3}{x - 5}

. State which

x

-value(s) are restricted and why.

2Task 2

Find the domain of

g (x) = \frac{x - 1}{x ^{2} - 4}

. State ALL restricted values.

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