Unformatted text preview: looking at in this section aren’t shifts, but
instead they are called reflections and there are two of them.
Reflection about the xaxis.
Given the graph of f ( x ) then the graph of g ( x ) =  f ( x ) is the graph of f ( x ) reflected
about the xaxis. This means that the signs on the all the y coordinates are changed to the
opposite sign.
Reflection about the yaxis.
Given the graph of f ( x ) then the graph of g ( x ) = f (  x ) is the graph of f ( x ) reflected
about the yaxis. This means that the signs on the all the x coordinates are changed to the
opposite sign.
Here is an example of each. Example 4 Using transformation sketch the graph of each of the following.
(a) g ( x ) =  x 2 [Solution]
(b) h ( x ) =  x [Solution] Solution
(a) Based on the placement of the minus sign (i.e. it’s outside the square and NOT inside the
square, or (  x ) ) it looks like we will be reflecting x 2 about the xaxis. So, again, the means
2 that all we do is change the sign on all the y coordinates.
Here is the sketch of this...
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 Spring '12
 MrVinh
 ........., Paul Dawkins

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