Transformations of Functions

1. Transformationsof Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology

2. Since the log1 = 0, a good reference point when graphing y = logx is (1,0) Notice, when graphing y=logx, the x-intercept is 1

3. Given the following function, If: a > 0, then shift the graph “a” units up, using the reference point (1,0) If: a < 0, then shift the graph “a” units down, using the reference point (1,0)

4. Given the following function, Since a > 0, then shift the graph “3” units up, using the reference point (1,0)

5. Let’s Graph

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12. Given the following function, We get the expression (x - b) and equal it to zero x - b = 0 x = b If: b> 0, then shift the graph “b” units to the right, using the reference point (1,0) If:b< 0, then shift the graph “b” units to the left, using the reference point (1,0)

13. Given the following function, x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit right, using the reference point (1,0)

14. Let’s Graph

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21. Graphing Recall: Shift “3” units up since 3 > 0 then we use the expression x + 1, and equal it to zero x +1 = 0 x = -1 Since –1 < 0, then we shift “1” unit to the left

22. Let’s Graph

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29. Given the following function, For this equation, c determines how wide or thin it will be. if: |c|>1, then the graph is closer to the y-axis if: |c|=1, then the graph remains the same if: 0<|c|<1, then the graph is further from the y-axis if c is a negative number, then the graph will reflect on the x-axis

30. Given the following function, Since |5| > 0, then the graph is closer to the y-axis

31. Let’s Graph

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40. Given the following function, Since 4 > 0, shift the graph “4” units up, using the reference point (1,0) x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit to the right, using the reference point (1,0). Since |5| > 0 shift the graph closer to the y-axis.

41. Let’s Graph

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