Linear Transformations Part 3
Linear Transformations Part 3 teaches how a base function can be transformed to generate a range of possible functions using algebraic, graphical, and verbal methods. The lesson explains how scaling, translation, and scaling on both the outside and inside of a function can be used to achieve complete linear transformation, and how it can be used to determine the transformation and vertex of a parabola. This form allows a base function to be transformed to generate a family of related functions.
Understand algebraically, graphically and verbally linear transformations of both the input and output of functions and how a base function can be linearly transformed to generate the whole set of possible functions of that type.
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- Notes - Notes from this lesson.
- Problem Set - A problem set from this lesson.
- Problem Set Solutions - Solutions to the problem set from this lesson.
- Graph Transformation Worksheet - A worksheet with graphs in which you must supply the equation for the graph.
- Graph Transformation Worksheet Key - Key to the graph transformation worksheet.
- What is a linear transformation of a function?
- How do you scale, flip, or translate a base function?
- How do you do linear transformations of the function f(x) = x^2?
- What happens when you add, subtract, multiply, and divide values to f(x) = x^2?
- What is the difference between adding numbers to the inside or outside of parentheses in a quadratic function?
- What does the function f(x) = -.11(x - 7.6)^2 + 7.8 look like when graphed?
- What is vertex form for a quadratic function and how can you read off the transformations that were done with the base function from it?
- How can you move a quadratic function up or down on a graph?
- How can you make a quadratic function wider or narrower?
- How do you flip a function upside down using transformations?
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Staff Review
This lesson pulls the previous two lessons together and shows you how to transform base functions using linear transformations. The concepts of translating, scaling, and flipping functions to fit data points are reviewed, and then you will see where these transformations fit in the functional notation. The problem set and worksheet really help with practicing the skills learned in this miniseries.
