121616949-math.29 - 1.4 Shifts and Dilations 15 Horizontal...

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1.4 Shifts and Dilations 15 Horizontal dilation. If x is replaced by x/A in a formula and A > 1 , then the effect on the graph is to expand it by a factor of A in the x -direction (away from the y -axis). If A is between 0 and 1 then the effect on the graph is to contract by a factor of 1 /A (towards the y -axis). We use the word “dilate” in both cases. For example, replacing x by x/ 0 . 5 = 2 x has the effect of contracting toward the y -axis by a factor of 2. If A is negative, we dilate by a factor of | A | and then flip about the y -axis. Thus, replacing x by - x has the effect of taking the mirror image of the graph with respect to the y -axis. For example, the function y = - x , which has domain x 0, is obtained by taking the graph of x and flipping it around the y -axis into the second quadrant. Vertical dilation. If y is replaced by y/B in a formula and B > 0 , then the effect on the graph is to dilate it by a factor of B in the vertical direction. Note that if we have a function y = f ( x ), replacing y by y/B
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