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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 x-axis.
Given the graph of f ( x ) then the graph of g ( x ) = - f ( x ) is the graph of f ( x ) reflected
about the x-axis. This means that the signs on the all the y coordinates are changed to the
Reflection about the y-axis.
Given the graph of f ( x ) then the graph of g ( x ) = f ( - x ) is the graph of f ( x ) reflected
about the y-axis. This means that the signs on the all the x coordinates are changed to the
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 x-axis. 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