Mississippi Math A3.A.9

MathGrades 9–12Algebra (A) Analyze and Manipulate Functions

The Standard

Determine the end behavior of polynomial functions.

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students use a polynomial’s highest-power term to tell whether its graph rises or falls on the left and right. They describe what happens as x gets very large or very negative.
What Mastery Looks Like: Given f(x) = -3x⁵ + 2x² - 1, a student says the left tail rises and the right tail falls. They explain that -3x⁵ controls the graph far from zero.
Common Misconceptions: Students may use the constant term or the last term written to decide the tail directions. Some think a negative leading coefficient makes both tails fall, even for an odd-degree polynomial.
How to Assess It: Exit ticket: For f(x) = -2x⁴ + 3x - 1 and g(x) = 4x³ - 7, label each tail as rising or falling. Circle the term that decides each answer.

Lesson moves

Give pairs graphs and equation cards for x⁴, -x⁴, x³, and -x³; have them match each graph to its equation.
Ask, “Why do 2x⁴ - 7x² + 3 and -2x⁴ - 7x² + 3 point in opposite directions at both ends?”
Post four tail-direction signs in classroom corners; show polynomial cards and have students move to the matching corner.
Use h(t) = -5t² + 20t for a tossed ball; ask what its tails predict and why negative heights do not fit the situation.

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