Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
The Parent Trap
The graphs are twins, but not identical, what’s the difference?
What transformed two similar objects into two different looks?
Lesson Summary
In this lesson, students will start by graphing a simple exponential function by
using a table. In the graphs that follow, students will be graphing more exponential
functions with various transformations. The students will be asked to analyze the graph
and make conjectures on what they think happens to the graph with alterations to the
parent function. The students will be using a graphing calculator to check their graphs
and their hypothesis on other parent functions and their transformations. To conclude
the inquiry lesson, students will be given a parent function and a transformed graph
and be asked to write the equation of the graph. As a challenge, students will be asked
to graph will multiple transformations. As an extension to this activity, students will be
able to generalize transformation rules to use with other functions.
Key Words
 Exponential Function
 Transformations
Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
 Graphing
Background Knowledge
Students will have knowledge of the following:

Graphing exponential functions using a table

Using a graphing calculator to graph functions
Ohio Standards
Benchmarks
Geometry and Spatial Sense
8-10: F: Represent and model transformation in a coordinate plane and describe
the results.
Patterns, Functions and Algebra
8-10: B: Identify and classify functions as linear or nonlinear and contrast their
properties using tables, graphs or equations.
8-10: C: Translate information from one representation (words, table, graph or
equation) to another representation of a relation or function.
Standards
Patterns, Functions and Algebra
Grade 9: #5: Describe and compare characteristics of the following families of
functions: linear, quadratic, and exponential functions; e.g. general shape, number of
roots, domain, range, rate of change, maximum or minimum.
Grade 11: #11: Describe how a change in the value of a constant in an
exponential, logarithmic or radical equation affects the graph of the equation.
Learning Objectives
 Students will use inquiry to determine how changes to a parent function affect its
graph.
 Students will analyze transformed graphs and be able to generate the function
that matches the graph given the equation of the parent function.
Project AMP
 Students will use a
transformations.
Dr. Antonio R. Quesada – Director, Project AMP
graphing
calculator
to
test
their
findings
about
Learning Goals
 Students will be able to sketch exponential graphs.
 Students will be able to sketch exponential graphs based on transformations
given to the parent function.
 Students will be able to analyze transformations in graphs.
 Students will be able to look at new graphs and develop equations given the
equation of the parent graph.
 Student will be able to generalize transformation rules and apply them to various
functions.
Materials
Pencil
Graphing Calculator
Activity Sheets
Assessment
At the end of this lesson, a transformed function will be put on the board. Then
students will be asked to sketch and describe the parent function. Then given a parent
function students will have to perform various transformations and write the related
equations.