http://www.ck12.org Chapter 1. Functions and Graphs
1.3 Point Notation and Function Notation
Here you will learn about the notation conventions involved with transformations.
When performing multiple transformations, it is very easy to make a small error. This is especially true when you
try to do every step mentally. Point notation is a useful tool for concentrating your efforts on a single point and helps
you to avoid making small mistakes.
What wouldf( 3 x)+7 look like in point notation and why is it useful?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/57853http://www.youtube.com/watch?v=An29CALYjAA James Sousa: Function Transformations: A Summary
Guidance
A transformation can be written in function notation and in point notation. Function notation is very common and
practical because it allows you to graph any function using the same basic thought process it takes to graph a parabola
in vertex form.
Another way to graph a function is to transform each point one at a time. This method works well when a table
ofx,yvalues is available or easily identified from the graph.
Essentially, it takes each coordinate(x,y)and assigns a new coordinate based on the transformation.
(x,y)→(new x,new y)
The newycoordinate is straightforward and is directly from what takes place outsidef(x)becausef(x)is just
another way to writey. For example,f(x)→ 2 f(x)−1 would have a newycoordinate of 2y−1.
The newxcoordinate is trickier. It comes from undoing the operations that affectx.
For example,f(x)→f( 2 x− 1 )would have a newxcoordinate ofx+ 21.
Example A
Convert the following transformation into function notation and point notation. Then, apply the transformation to
the three points in the table. Transformation: Horizontal shift right three units, vertical shift up 4 units.
TABLE1.1:
x y
1 3