2.2.1 Transforming Linear Functions (continued) Example 2 Rotating Linear Functions
A rotation is a type of transformation that rotates every point on a graph about a particular point. To describe a rotation of a line, state whether the line is rotated clockwise or counterclockwise, and state the point about which the line is rotated. Changing the slope m in the function f ( x ) = mx + b causes a rotation of the line about the point (0, b ), which changes the line’s steepness.
Example 3 Reflecting Linear Functions A reflection is a transformation that produces a mirror image of the graph across a line of reflection. If a point ( x , y ) is reflected across the y -axis, the result is ( − x , y ). Use the following steps to reflect a line across the y -axis. 1. Pick two points on the line and find the reflection of each point across the y -axis. 2. Plot those two reflection points. 3. Draw a line through the two reflection points. Changing the slope m in the function f ( x ) = mx + b to f ( x ) = − mx + b causes the line to be reflected across the y -axis.
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