Students analyze the graphs of polynomial and rational functions — predicting end behavior from the degree and leading coefficient, and finding the asymptotes and zeros that define a rational function’s shape.
Students will be able to…
Just by glancing at a function’s equation, an expert can sketch where its graph rises, falls, and shoots to infinity. What clues make that possible?
Project each item and have students predict end behavior, zeros, and asymptotes. The tool explains how degree and structure shape the graph.
Tap any phase to open the teacher moves and student actions.
How can an expert sketch a graph just from its equation?
Teacher models.
Class uses Analyze the Function.
Students analyze functions.
One function.
Aligned to the Common Core State Standards for Mathematics (High School: Precalculus).
Graph polynomial functions, identifying zeros and end behavior.
Graph rational functions, identifying zeros and asymptotes.
Identify zeros of polynomials and use them to sketch a graph.
Rewrite rational expressions.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students determine horizontal asymptotes of rational functions by comparing the degrees of the numerator and denominator. A printable functions sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.