Linear Transformations Part 1
In this lesson on linear transformations, students learn how to use scaling, flipping, and translating to transform a base function like x-squared. Linear transformations allow students to move a function up and down, left and right, and adjust the width of the function, giving them the ability to fit a quadratic model more accurately. Adding a value to the outside of a function translates it up or down, while adding or subtracting something to the input side moves a function left or right. These translations are part of a linear transformation, which students can use to generate a whole set of possible 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?
- How can you determine the quadratic function of a parabola from a graph that has been transformed?
- 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?
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Staff Review
This lesson shows you how to transform base functions using linear transformations. The concepts of translating, scaling, and flipping functions to fit data points are explained, and then you will learn where these transformations fit in the functional notation. The problem set and worksheet really help with practicing the skills learned in this miniseries.
