SECONDARY MATH TRANSFORMATIONS

Transcription

1 SECONDARY MATH TRANSFORMATIONS

2 WARM UP

3 WHAT YOU WILL LEARN How to transform functions from the parent function How to describe a transformation How to write an equation of a transformed function

4 There are several tpes of functions (linear, quadratic, absolute value, sine, cosine, eponential, cubic, etc.). Each of these can be considered a famil with unique characteristics that are shared among the members. The parent function is the most basic function in each famil. It is used to create more complicated functions.

5 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, Shifting (translating) the graph left or right vertical stretching or shrinking (making the graph more steep or less steep) Reflecting across -ais or -ais

6 GRAPHICAL TRANSFORMATIONS = = + Compare the two parabolas. Adding or Subtracting a number from the parent function moves the graph up or down.

7 = Wh does adding to the parent function translate the graph up b? = + Build a table of values for each equation for domain elements: -, -, 0,,

8 YOUR TURN: Describe the transformation to the parent function: = = 4 translated down 4 = + 5 translated up 5 What ke feature is affected b a vertical shift? Range

9 GRAPHICAL TRANSFORMATIONS = = 3 Compare the two parabolas. Multipling the -values of the parent function b 3, makes it 3 times as steep.

10 = Wh does multipling the parent function b 3 cause the parent to be verticall stretched b a factor of 3?. = 3 Build a table of values for each equation for domain elements: -, -, 0,, What values are affected b a vertical stretch? The values. You multipl the values b the stretch factor

11 GRAPHICAL TRANSFORMATIONS = = Multipling the parent function b -, reflects across the -ais. Compare the two parabolas.

12 YOUR TURN: Describe the transformation to the parent function: = = + Reflected across -ais and translated up = 3 6 Verticall stretched b a factor of 3 and translated down 6 What ke feature is affected b a reflection across the -ais? Maimum or minimum

13 GRAPHICAL TRANSFORMATIONS = = ( ) Compare the two parabolas. Adding or Subtracting a number to the variable of the parent function moves the graph left right. What ke feature ma be affected b a horizontal shift? Domain

14 = Wh does replacing with translates the parent function right b. = ( ) Build a table of values for each equation for domain elements: -, -, 0,,

15 QUADRATIC TRANSFORMATIONS ) = ( ) a( h + k Reflection across -ais vertical stretch factor Translates left/right translating up or down = ( 3) + 4 Reflected across -ais, twice as steep, translated up 4, translated right 3

16 DESCRIBE THE TRANSFORMATION FROM THE PARENT FUNCTION AND THEN WRITE THE EQUATION FOR THE FOLLOWING GRAPHS. translated up 3 translated left 5 = ( + 5) + 3 Verticall stretched b a factor of, translated right = ( )

17 YOUR TURN: Describe the transformation to the parent function: = = ( + 3) + 4 Reflected across -ais Verticall stretched b a factor of ½ (shrunk), translated up 4 translated left 3

18 Absolute Value Transformation = ( ) a h + k Reflection across -ais Vertical stretch factor Translates left/right translating up or down

19 YOUR TURN: = What is the transformation to the parent function? = 3 translated right 3 = Verticall stretched b a factor of Twice as steep Slope on right side is + slope on left side is -

20 YOUR TURN: = What is the transformation to the parent function? = Reflected across -ais Vertical stretch b a factor of 3 times as steep Left up 4

21 Square Root Transformation = ( ) a h + k Reflection across -ais Vertical stretch factor Translates left/right translating up or down

22 = 4 + Up 4, right = + 4 Notice that both equations are the same equation. = Down 3, reflected across -ais, Vertical stretch b a factor of left 3

23 What does adding or subtraction k do to the parent function? f ( ) = + k Vertical shift What does adding or subtraction h do to the parent function? f ( ) = h What does multipling b a do to the parent function? f ( ) = a Horizontal shift Vertical stretch What does multipling b (-) do to the parent function? f ( ) = Reflection across -ais