Student Sheet
Transformations of Functions
Topic: Transformations of parent functions
Introduction: Have you ever seen Terminator 2, The Mask, or The Matrix? These were
among the first to films to use spectacular effects in which a character or object having one
shape was transformed in a fluid fashion into quite a different shape. The name for such a
transformation is morphing. The effect allows a real actor to be seamlessly transformed into a
computer-generated animation. The animation can be made to perform impossible feats before
being morphed back to the conventionally filmed image.
Precalculus, by Robert Blitzer. Miami-Dade CC. Prentice-Hall, 2001
Transformations allow one functions graph to be shifted vertically or horizontally,
reflected about the x-axis or the y-axis, stretched or shrunk, or a combination of these. Knowing
these techniques is useful when modeling real-life data.
Materials Needed: Graphics Calculator, Parent Functions Graphs
Student Procedure: Given the equation of a function by the instructor, students will graph
the equation on the graphics calculator. Discuss the effects of various transformations of the
parent function. Students will then stand up, and with their bodies demonstrate the parent
function and any transformations, which are illustrated by the equation the instructor gives to the
class.
Extension/Report: Sketch the graphs of the given equations and write the equations of the
given graphs.
Student Handouts: Parent function graph and Graphing worksheet
Teacher Sheet
Transformations of Functions
Course: MAT 171 / MAT 175
Math Topics: Functions and Transformations
Intellectual Development Standards: Modeling, Using Technology, and Reasoning
Pedagogy standards: Teaching with Technology, Experiencing Mathematics, Interactive
Learning.
Goals and Objectives:
The student will be able to:
 Learn basic parent functions
 Use vertical shifts to graph functions.
 Use horizontal shifts to graph functions.
 Use reflections to graph functions.
 Use vertical stretching and shrinking to graph functions.
 Graph functions involving a sequence of transformations.
Procedure Hints: The instructor could distribute parent function graphs and familiarize the
students with the graphs. Then using graphing calculators, give students several equations to
illustrate various transformations. Have the class discuss and determine what general effects
these equation changes have on the basic parent function. You might derive equations such as
y = f(x) + c (etc.). After general effects are discovered, the class will stand up and model with
their bodies, equations given by the instructor. To culminate the activity, students will work
individually on the worksheet provided. (If you teach this topic before exponential, log, and trig
function, you should delete / omit these functions from the activity.)
TRANSFORMATION
STUDENT GRAPHING WORKSHEET
Sketch the following pairs of functions on the same graph. Answer the questions following each
group of graphs. Use a window of [ -5, 5 ] and [-5,5]. Your calculator should be in radian
mode.
Group I
A)
f ( x)  x 2
g ( x)  x 2  3
B)
f ( x)  x
g ( x)  x  4
C)
f ( x)  cos( x)
g ( x)  cos( x)  2
What happened to the graph of f(x) to produce the graph of g(x)?
Group II
A)
f ( x)  x 2
g ( x)  ( x  2) 2
B)
f ( x)  x
g ( x)  x  3
C)
What happened to the graph of f(x) to produce the graph of g(x)?
f ( x)  x
g ( x)  x  4
Group III
f ( x)  int( x)
A)
g ( x)  .5 int( x)
B)
f ( x)  cos( x)
C)
g ( x)  3 cos( x)
f ( x)  x
g ( x)  2 x
What happened to the graph of f(x) to produce the graph of g(x)?
Group IV
f ( x)  x 2
A)
g ( x)  (3x) 2
B)
f ( x)  int( x)
g ( x)  int(2 x)
C)
f ( x)  cos( x)
g ( x)  cos(0.5 x)
What happened to the graph of f(x) to produce the graph of g(x)?
Group V
A)
f ( x)  x 2
g ( x )  ( x ) 2
B)
f ( x)  int( x)
g ( x)   int( x)
C)
f ( x)  cos( x)
g ( x)   cos( x)
What happened to the graph of f(x) to produce the graph of g(x)?