Algebra II Lesson

Stacked Discounts & Inverses: Composing and Undoing Functions

Shared by A STEM Educator

11th GradeBTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.HSF.BF.A.1c, CCSS.MATH.CONTENT.HSF.BF.B.4a, CCSS.MATH.CONTENT.HSF.BF.B.4b50 min

Learning Objective

Students will compose functions algebraically and graphically, find inverse functions by undoing operations, verify inverses via composition, and identify domain restrictions for one-to-one compliance.

Lesson Overview

Students discover function composition through stacked retail discounts with sales tax, then systematically build toward finding and verifying inverse functions with domain restrictions using mapping diagrams, tables, and graph symmetry across y = x.

Materials

Vertical whiteboards or large paper on desks
Dry-erase markers (one per group)
Pencils and notebook paper
Basic calculator or phone calculator

Scaffolded Task Progression

1Task 1

A store applies a 20% discount function:

d (p) = 0.8 p

, where

p

is the original price in dollars.

Fill in the mapping diagram and table:

Original Price $p$	Discounted Price $d (p)$
50
80
120
200

Then evaluate:

d (150)

= ?

2Task 2

Now the store also charges 8% sales tax AFTER the discount. The tax function is:

t (q) = 1.08 q

, where

q

is the price after discount.

Using your results from Task 1, apply the tax function to each discounted price:

$p$	$d (p)$	$t (d (p))$
50	40
80	64
120	96
200	160

What single expression gives

t (d (p))

directly in terms of

p

Unlock the full lesson

See all 7 scaffolded tasks, the full answer key, warm-up, exit slip, and a print-ready version — free to start.

Create a free account

Already have an account? Sign in

Make it your own

Like this lesson but want to tweak it?

Make an editable copy and adjust the tasks, warm-up, and answer key to fit your class — no need to start from scratch.

Generate a new lesson