http://www.ck12.org Chapter 1. Functions and Graphs
1.2 Graphical Transformations
Here you will learn how a graph changes when you change its equation by adding, subtracting, and multiplying by
constants.
The basic functions are powerful, but they are extremely limited until you can change them to match any given
situation. Transformation means that you can change theequationof a basic function by adding, subtracting, and/or
multiplying by constants and thus cause a corresponding change in thegraph. What are the effects of the following
transformations?
1)f(x)→f(x+ 3 )
2)h(x)→h(x)− 5
3)g(x)→−g( 2 x)
4)j(x)→j(−x 2 )
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/http://www.youtube.com/watch?v=CESXLJaq6Mk James Sousa: Function Transformations: Horizontal and Verti-
cal Translations
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/http://www.youtube.com/watch?v=2S9LUinJ8-w James Sousa: Function Transformations: Horizontal and Vertical
Stretch and Compression
Guidance
A function is a rule that takes any inputxand gives a specific output. When you use letters likef,g,h, orjto describe
the rule, this is called function notation. In order to interpret what effect the algebraic change in the equation will
have on the graph, it is important to be able to read those changes in general function notation and then apply them
to specific cases.