2. Lesson 1-6 Graphical Transformations

3. Graphical Transformations
Transformation: an adjustment made to the parent function that results in a change to the graph of the parent function.
Changes could include:
shifting (“translating”) the graph up or down,
“translating” the graph left or right
vertical stretching or shrinking
(making the graph more steep or less steep)
Reflecting across x-axis or y-axis

4. Graphical Transformations
Parent Function: The simplest function in a family
of functions (lines, parabolas, cubic functions, etc.)
Compare the two parabolas.

5. Why does adding 2 to the parent function shift the graph up by 2?
Build a table of values for each equation for domain elements: -2, -1, 0, 1, 2. x y -2 -1 1 2 x y -2 -1 1 2 4 6 1 3 2 1 3 4 6

6. Your Turn: Describe the transformation to the parent function:
translated down 4
Describe the transformation to the parent function:
translated up 5

7. Graphical Transformations
Compare the two parabolas.
Multiplying the parent function by 3, makes it 3 times as steep.

8. Why does multiplying the parent function by 3 cause the parent to be vertically stretched by a factor of 3?.
Build a table of values for each equation for domain elements: -2, -1, 0, 1, 2. x y -2 -1 1 2 x y -2 -1 1 2 12 4 3 1 3 1 12 4

9. Graphical Transformations
Multiplying the parent function by -1, reflects across the x-axis.
Compare the two parabolas.

10. Your Turn: Describe the transformation to the parent function:
Reflected across x-axis and translated up 2
Describe the transformation to the parent function:
Vertically stretched by a factor of 3 and translated down 6

11. Graphical Transformations
Compare the two parabolas.

12. Why does replacing ‘x’ with ‘x – 1’ translates the parent function right by 1.
Build a table of values for each equation for domain elements: -2, -1, 0, 1, 2. x y -2 -1 1 2 x y -2 -1 1 2 9 4 4 1 1 1 1 4

13. Quadratic Transformations
translating up or down
Reflection across x-axis
vertical stretch factor
Translates left/right
Reflected across x-axis, twice as steep, translated up 4, translated right 3

14. translated up 3 translated left 5
Your Turn:
Describe the transformation to the parent function:
translated up translated left 5

15. Vertically stretched by a factor of 2, translated right 1
Your Turn:
Describe the transformation to the parent function:
Vertically stretched by a factor of 2, translated right 1

16. Your Turn: Describe the transformation to the parent function:
Reflected across x-axis
Vertically stretched by a factor of ½ (shrunk), translated up 4
translated left 3

17. Absolute Value Function
Why does it have this shape?

18. Your turn: What is the transformation to the parent function?
translated right 3
Vertically stretched by a factor of 2  Twice as steep
Slope on right side is +2 slope on left side is -2

19. Reflected across x-axis
Your turn:
What is the transformation to the parent function?
Reflected across x-axis
VSF = 4  4 times as steep
Left 2
up 4

20. Absolute Value Transformation
Vertical stretch factor
Translates left/right
translating up or down
Reflection across x-axis

21. Reflection across x-axis
What does adding or subtraction “k” do to the parent function?
Vertical shift
What does adding or subtraction “h” do to the parent function?
Horizontal shift
What does multiplying by ‘a’ do to the parent function?
Vertical stretch
What does multiplying by (-1) do to the parent function?
Reflection across x-axis

22. Square Root Function
What is the domain of the graph?

23. Describe the transformation to the parent function:
Up 4, right 2
Down 3, reflected across x-axis, VSF= left 3

24. Reflecting Across the x-axis

25. Reflecting across the y-axis

26. example

27. Question:
What happens when an even function is reflected across the y-axis?

28. Homework:
HW 1-6 pg 147: 2-32 Even