1. Parent Functions and Transformations
Parent Function – simplest form of a type (or family) of graphs Using a parent function you can transform the graph to create other graphs of the same family.

2. Parent Functions

3. Translation

6. Translation

9. Practice
Graph
Graph y = |x+2| + 2

12. y = |x+2| + 2

13. 4 3 5
6 Same as original

14. 15 right 3, up 2, left 6 15 17 19

15. 7 8 9

16. Reflection
When the parent function is multiplied by -1 the result, -f(x) is a reflection across the x axis
The figures flips over the line of reflection

17. A graph can be reflected across any line including the x-axis, y-axis, origin, y=x, etc.

20. Practice
Graph y= -|x-1|-2

21. Dilation
A dilation shrinks or enlarges a graph proportionally. When a function is multiplied by a nonzero number the slope changes which stretches or compresses the graph.
Coefficients over 1 cause the graph to be stretched vertically.
Coefficients between 0 and 1 cause the graph to be compressed vertically.

22. y=3|x|
y=|x|
y= ½ |x|

23. Horizontal dilation
When the variable is multiplied by a nonzero coefficient, the graph is stretched or compressed horizontally.

24. y=x
y=½x

25. Summary of Transformations