Montana Math MT.PLUS.ALG.FUN.2

MathGrades 9–12Functions, Expressions, and Inequalities

The Standard

Understand the relationship between a function and its inverse.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students reverse a function's inputs and outputs to find its inverse rule, table, or graph. They check whether the reverse still gives just one output for each input.
What Mastery Looks Like: Given f(x)=2x+3, a student finds f⁻¹(x)=(x−3)/2 and checks that f⁻¹(f(4))=4. They can explain why x² needs a restricted domain before its reverse is a function.
Common Misconceptions: Students may read f⁻¹(x) as 1/f(x). They may call √x the inverse of x² on all real numbers, missing that both 2 and −2 produce 4.
How to Assess It: Ask students: For f(x)=3x−6, find the inverse rule and use 4 to check that it reverses the original rule.

Lesson moves

Give pairs cards marked 0→3, 1→5, and 2→7; have them reverse each arrow and write a rule for the new table.
Ask: Why can't y=x² have an inverse function for all real inputs? Use −2 and 2 in your explanation.
Play an inverse match game with rule cards and input-output cards; require students to check each match by applying both rules.
Give students F=(9/5)C+32 and the readings 32°F and 68°F; have them find the Celsius readings by reversing the rule.

Free download

$Preview of the MT.PLUS.ALG.FUN.2 printable worksheet$

A ready-to-print activity worksheet aligned to MT.PLUS.ALG.FUN.2, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.