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
stretch/compress
shift
reflect

3. Graph the parent function using a table of values1.

4. Graph the parent function using a table of values2.

5. Graph the parent function using a table of values3.

6. Graph the parent function using a table of values4.

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

8. Vertical Shifts vertical up down same up down inside
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.
down
same up
down
inside

9. When looking at the equation of a parent function, a vertical shift is
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 horizontal left right opposite left right always
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.
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.