PRECALCULUS GRAPHING TRANSFORMATIONS LAB
The purpose of this lab is to investigate both rigid (shape preserving) and non-rigid
(shape changing) function transformations. Rigid Transformations include translations
(shifting) and reflections. Non-rigid Transformations include scaling (dilations and
compressions).
Use of a graphing calculator or a computer with graphing software is recommended for
this lab. Directions for using Maple V, Release 5, are available on the web site. If using a
calculator, either see owner's manual for guidance or ask for assistance in the Math Lab.
I. RIGID TRANSFORMATIONS.
A. Translations of the form f (x) + k.
On the same axes below, graph and label the following three functions:
1. f (x) = | x |
2. f (x) + 3
3. f (x) - 6
How is f (x) shifted to get f (x) + k ?
B. Translations of the form f (x - h).
On the same axes, graph and label the following three functions:
1. f (x) = x³
2. f (x + 4)
How is f (x) shifted to get f (x - h) ?
3. f (x - 5)
C. Combined Translations of the form f (x - h) + k.
On the same axes, graph and label the following two functions:
1. f (x) = | x |
2. f (x + 2) - 3
Explain the transformation f (x + 2) - 3.
For any given h and k, how is f (x) transformed into f (x - h) + k ? (Hint: experiment
with different values for h and k using your calculator)
D. Reflections of the form - f (x).
On the same axes, graph and label the following two functions:
1.
2. - f (x)
What is f (x) reflected about to get -f (x) ?
E. Reflections of the form f (-x ).
On the same axes, graph and label the following:
1.
2. f (-x )
What is f (x) reflected about to get f (-x ) ?
II. NON-RIGID TRANSFORMATIONS.
A. Vertical Stretches of the form a·f (x), where a is greater than 1.
On the same axes, graph and label the following three functions:
1. f (x) = x²
2. 3·f (x)
3. 10·f (x)
What happens to the graph when f (x) is multiplied by a constant larger than 1?
B. Vertical Compressions of the form a·f (x), where a is between 0 and 1.
On the same axes, graph and label the following three functions:
1. f (x) = x²
2. 0.5·f (x)
3. 0.2·f (x)
What happens to the graph when f (x) is multiplied by a constant between 0 and 1 ?
III. GENERAL FORM a·f (x - h) + k.
Suppose that the graph of
is transformed as follows:
• It is shifted to the right 2 units.
• It is reflected about the x-axis.
• It is stretched by a factor of 3.
• It is shifted up 1.5 units.
1. Graph and label f (x) and the resulting function on the same axes.
2. Write the equation for the function which results from the above changes.
IV. Let the graph of some function F(x) be given as follows:
Based on the graph of F(x), graph the following. Label the x- and y-coordinates of the
points corresponding to the labeled points of F(x).
A. - F(x) +2
C. 3·F(x)
B. F(- x)
D. F(x + 4) - 2