http://www.ck12.org Chapter 1. Functions and Graphs
Convert the following point notation to words and to function notation and then apply the transformation to the
included table of points.
(x+ 3 ,y− 1 )→( 2 x+ 6 ,−y)
TABLE1.3:
x y
10 8
12 7
14 6Solution: This problem is different because it seems like there is a transformation happening to the original left
point. This is an added layer of challenge because the transformation of interest is just the difference between the
two points. Notice that thexcoordinate has simply doubled and theycoordinate has gotten bigger by one and turned
negative. This problem can be rewritten as:
(x,y)→( 2 x,−(y+ 1 )) = ( 2 x,−y− 1 )
f(x)→−f(x 2 )− 1
Concept Problem Revisited
The functionf( 3 x)+7 would be written in point notation as(x,y)→(x 3 ,y+ 7 ). This is useful because it becomes
obvious that thexvalues are all divided by three and theyvalues all increase by 7.
Vocabulary
Notationis a mathematical convention that helps others read your work. It is supposed to be designed to help aid
your thinking, but when misunderstood can cause great confusion.
Guided Practice
- Convert the following function notation into words and then point notation. Finally, apply the transformation to
three example points.
f(x)→− 2 f(x− 1 )+ 4 - Convert the following function in point notation to words and then function notation.
(x,y)→( 3 x+ 1 ,−y+ 7 ) - Convert the following function in function notation to words and then point notation.