The document discusses graphs of the form y = x^n where n is an integer greater than 1. It notes that the graphs can first be sketched by noticing that all points where the curve cuts the x-axis are stationary points, and the curve has the same sign as the given value of n for any x. The graphs are also affected by whether n is odd or even.

1. (H)Graphs of the Form   n
xfy 
where n>1 and an integer
    
noticing;and
drawingfirstbysketchedbecanofgraphThe xfyxfy
n


2. (H)Graphs of the Form   n
xfy 
where n>1 and an integer
    
noticing;and
drawingfirstbysketchedbecanofgraphThe xfyxfy
n

pointsstationarybestillmustpointsstationaryall

3. y
x
1
-1
 xfy    2
xfy 

4. y
x
1
-1
 xfy    2
xfy 

5. (H)Graphs of the Form   n
xfy 
where n>1 and an integer
    
noticing;and
drawingfirstbysketchedbecanofgraphThe xfyxfy
n

pointsstationarybestillmustpointsstationaryall
pointsstationaryalsoareaxisthecutscurvethewherepointsall x

6. y
x
1
-1
 xfy    2
xfy 

7. y
x
1
-1
 xfy    2
xfy 

8. y
x
1
-1
 xfy    2
xfy 

9. (H)Graphs of the Form   n
xfy 
where n>1 and an integer
    
noticing;and
drawingfirstbysketchedbecanofgraphThe xfyxfy
n

pointsstationarybestillmustpointsstationaryall
pointsstationaryalsoareaxisthecutscurvethewherepointsall x
      xfxfxf
n
 then1if

10. (H)Graphs of the Form   n
xfy 
where n>1 and an integer
    
noticing;and
drawingfirstbysketchedbecanofgraphThe xfyxfy
n

pointsstationarybestillmustpointsstationaryall
pointsstationaryalsoareaxisthecutscurvethewherepointsall x
      xfxfxf
n
 then1if
      xfxfxf
n
 then1if

11. y
x
1
-1
 xfy    2
xfy 

12. y
x
1
-1
 xfy    2
xfy 

13. y
x
1
-1
 xfy    2
xfy 

14. y
x
1
-1
 xfy    2
xfy 

15. (H)Graphs of the Form   n
xfy 
where n>1 and an integer
    
noticing;and
drawingfirstbysketchedbecanofgraphThe xfyxfy
n

pointsstationarybestillmustpointsstationaryall
pointsstationaryalsoareaxisthecutscurvethewherepointsall x
      xfxfxf
n
 then1if
      xfxfxf
n
 then1if
   0even thenisif 
n
xfn

16. (H)Graphs of the Form   n
xfy 
where n>1 and an integer
    
noticing;and
drawingfirstbysketchedbecanofgraphThe xfyxfy
n

pointsstationarybestillmustpointsstationaryall
pointsstationaryalsoareaxisthecutscurvethewherepointsall x
      xfxfxf
n
 then1if
      xfxfxf
n
 then1if
   0even thenisif 
n
xfn
     xxfxfn
n
ofegiven valuanyforofsignsametheisthenoddisif

17. y
x
1
-1
 xfy    3
xfy 

18. y
x
1
-1
 xfy    3
xfy 

19. y
x
1
-1
 xfy    3
xfy 

20. y
x
1
-1
 xfy    3
xfy 

21. y
x
1
-1
 xfy    3
xfy 

22. y
x
1
-1
 xfy    3
xfy 

23. y
x
1
-1
 xfy    3
xfy 

24. y
x
1
-1
 xfy    3
xfy 