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Math 1050 Lab: Graphing Transformations with Maple, Lab Reports of Algebra

Salt Lake Community CollegeAlgebra

Instructions for a lab in math 1050 where students use maple to investigate rigid and non-rigid function transformations, including translations, reflections, vertical stretches, and compressions.

Typology: Lab Reports

Pre 2010

Uploaded on 08/13/2009

koofers-user-eoi
koofers-user-eoi 🇺🇸

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Math 1050 GRAPHING TRANSFORMATIONS LAB
With Maple Instructions
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). The directions are for using Maple V, Release 5, available on the
computers in the Math Lab.
To Begin: 1. Turn on the computer.
2. Type username: math. Leave password blank. Press the Enter key.
3. Once in Maple, type and enter: with (plots):
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
Type and enter: f:=x -> abs(x);
plot ({f(x)}, x = -10..10, y = -10..10);
How is f (x) shifted to get f (x) + k ?
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Math 1050 GRAPHING TRANSFORMATIONS LAB

With Maple Instructions

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). The directions are for using Maple V, Release 5, available on the computers in the Math Lab. To Begin: 1. Turn on the computer.

  1. Type username: math. Leave password blank. Press the Enter key.
  2. Once in Maple, type and enter: with (plots): I. RIGID TRANSFORMATIONS. A. Translations of the form f (x) + k. On the same axes below, graph and label the following three functions:
  3. f (x) = | x | 2. f (x) + 3 3. f (x) - 6 Type and enter: f:=x -> abs(x); plot ({f(x)}, x = -10..10, y = -10..10); 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) 3. f (x - 5) Type and enter: f:=x -> x^3; plot ({f(x)}, x = -10..10, y = -10..10); How is f (x) shifted to get f (x + h)?

D. Reflections of the form - f (x). On the same axes, graph and label the following two functions:

      • f (x) Type and enter: f:=x -> 3^x; plot ({f(x)}, x = -10..10, y = -10..10); 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. f (-x ) Type and enter: f:=x -> 3^x; plot ({f(x)}, x = -10..10, y = -10..10); What is f (x) reflected about to get f (-x )?

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) (See instructions for A.) 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. Type and enter: f:=x -> sqrt(x); plot ({f(x)}, x = 0..6, y = -3..3);
  2. Write the equation for the function which results from the above changes.