Graphing Techniques
FIU has online movies to help with this topic on this page. You must have QuickTime Player, a free download, installed on your computer.
The order of operations is the key to determining whether a shift is vertical or horizontal. If a number is added or subtracted after the function rule is performed, the shift is vertical. For example, in the equation y = x2 + 2, the 2 is added after the squaring is performed, so it shifts the graph of y = x2 vertically. Vertical shifts go in the same direction as the sign, so this shift is 2 units up. If a number is added or subtracted before the function rule is performed, the shift is horizontal. For example, in the equation y = (x + 2)2, the 2 is added before the squaring is done, so it shifts the graph of y = x2 horizontally. Horizontal shifts go in the opposite direction of the sign, so this shift is 2 units to the left (in the negative direction).
The University of Idaho provides another online resource. These lectures are only viewable by those with DSL or cable modems. Real Player, a free download, is required to see these videos. The videos cover the topics below. To see the videos, go to this page and look under section 3.5.
Vertical and
horizontal shifts
Compressing and Stretching a function
Reflection of functions
about the x-axis and y-axis
Horizontal Stretches and Compressions
A summary
of transformations
Graph
functions using compressions and stretches
An
example illustrating a compression and stretch
Graph
functions using reflections about the x-axis or y-axis
Summary
of transformations plus and example
Other online help:
Graphing
Techniques