Algebra 2 Lesson

Piecewise Functions: Building Graphs One Piece at a Time

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10th grade level IIIBTC Style / Thinking Classrooms70 min

Learning Objective

Students will graph piecewise-defined functions on a coordinate plane, correctly applying domain restrictions, open/closed endpoints, and interpreting the function's behavior across all pieces.

Lesson Overview

Students progress from reading and evaluating piecewise functions to graphing multi-piece functions with restricted domains, including step functions and functions with continuity analysis. Tasks change one variable at a time, building from single-piece evaluation to full graph construction and interpretation.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors if available)
Pencils and blank paper for notes

Scaffolded Task Progression

1Task 1

A piecewise function is defined as:

f (x) = {2 x + 1 7 if x < 2 if x \geq 2

Evaluate:

f (0)

f (2)

, and

f (5)

2Task 2

Using the same function:

f (x) = {2 x + 1 7 if x < 2 if x \geq 2

Evaluate:

f (- 3)

f (1.9)

, and

f (2)

.

What output does the first piece approach as

x

gets close to

2

from the left? What does the second piece equal at

x = 2

3Task 3

Graph ONLY the first piece of the function below over its domain. Do not graph the second piece yet.

f (x) = {2 x + 1 7 if x < 2 if x \geq 2

What kind of circle (open or closed) belongs at

x = 2

? Why?

[ Interactive graph / diagram, available in the full lesson ]

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