Section 1.3 Transformations of Equations and Functions Math 131 J. Lewis
2
Consider the graph of the parabola y  x . We can make any parabola by transforming this function
by shifting right or left, up or down, or stretching and or reflecting.
Example1: y  ( x  2 )
2
2
is the parabola y  x shifted to the right two units.
Make tables of x and y values to see why the graph is shifted to the right.
2
2
Example2: y  3 ( x  1) This is y  x shifted to the right one unit and vertically stretched by a
factor of 3.
Example3: y 
1
2
2
( x  1)  5 Write the transformations that transform y  x to this function.
2
Which one must be done last?
Example 4:
y
1
2
2
( x  1)  5
Example 5: List transformations of y 
x , in a proper order, which result in y  2 3 x  6  7 .
There are different ways to do this.
Example 6: List transformations of y 
Example 7: Describe the graph of
x , in a proper order, which result in y   2 3 x  6  4 .
( x  2)
4
2

( y  1)
9
2
 1 as a transformation of the unit circle.