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PARENT FUNCTIONS & TRANSFORMATIONS.  Parent functions are common functions of algebra that we.  A is when we, or a graph. The graph maintains the same.

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Presentation on theme: "PARENT FUNCTIONS & TRANSFORMATIONS.  Parent functions are common functions of algebra that we.  A is when we, or a graph. The graph maintains the same."— Presentation transcript:

1 PARENT FUNCTIONS & TRANSFORMATIONS

2  Parent functions are common functions of algebra that we.  A is when we, or a graph. The graph maintains the same general characteristics, but it morphed. transform transformation shiftreflect stretch/compress

3 Graph the parent function using a table of values 1.

4 Graph the parent function using a table of values 2.

5 Graph the parent function using a table of values 3.

6 Graph the parent function using a table of values 4.

7  A is a slide. When we graph translations, we will the graph from one location to another. translation shift

8 Vertical Shifts  A shift moves the graph or.  If is our function, the graph of is the graph of shifted c units vertically upward.  If is our function, the graph of is the graph of shifted c units vertically downward.  Note: with vertical shifts, the sign on the movement (+/-) is the direction as what the shift is. So, if the sign is positive we go and when the sign is negative we go.  Vertical shifts are never the parentheses. verticalup down same up down inside

9  When looking at the equation of a parent function, a vertical shift is grouped with the x. not

10 Graph the function 5.

11 Graph the function 6.

12 Horizontal Shifts  A shift moves the graph or.  If is our function, the graph of is the graph of shifted c units horizontally to the left.  If is our function, the graph of is the graph of shifted c units horizontally to the right.  Note: with horizontal shifts, the sign on the movement (+/-) is the direction as what the shift is. So, if the sign is positive we go and when the sign is negative we go.  Horizontal shifts are inside the parentheses. horizontal left right opposite left right always

13 Graph the function 7.

14 Graph the function 8.

15 Vertical Reflections  A reflection is a reflection about the.  The graph of is the graph of reflected about the x-axis.  In other words, if there is a out front, we flip over the. vertical x-axis negative x-axis

16 Graph the function 9.

17 Graph the function 10.

18 Combining Shifts and Reflections  We can graph both a vertical and horizontal shift at the same time.  Just remember the vertical movement is the parentheses, and the horizontal movement is the parentheses.  A vertical reflection will also be the parentheses.  Order of transformations – work from the inside out!  Horizontal Shift  Vertical Reflection  Vertical Shift outside inside outside

19 Graph the function 11.

20 Graph the function 12.

21 Graph the function 13.

22 Graph the function 14.


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