The document describes how to sketch the graph of y = [f(x)]n, where n is an integer greater than 1. It notes that the graph can be drawn by first sketching y = f(x) and observing that: stationary points and x-intercepts remain; [f(x)]n is greater than f(x) if f(x) > 1, and less if f(x) < 1; if n is even, [f(x)]n is always positive; if n is odd, [f(x)]n has the same sign as f(x).

1. (H)Graphs of the Form y   f  x 
n
where n>1 and an integer
The graph of y   f  x  can be sketched by first drawing y  f  x 
n
and noticing;

2. (H)Graphs of the Form y   f  x 
n
where n>1 and an integer
The graph of y   f  x  can be sketched by first drawing y  f  x 
n
and noticing;
 all stationary points must still be stationary points

3. y  f x y   f  x 
2
y
1
x
-1

4. y  f x y   f  x 
2
y
1
x
-1

5. (H)Graphs of the Form y   f  x 
n
where n>1 and an integer
The graph of y   f  x  can be sketched by first drawing y  f  x 
n
and noticing;
 all stationary points must still be stationary points
 all points where the curve cuts the x axis are also stationary points

6. y  f x y   f  x 
2
y
1
x
-1

7. y  f x y   f  x 
2
y
1
x
-1

8. y  f x y   f  x 
2
y
1
x
-1

9. (H)Graphs of the Form y   f  x 
n
where n>1 and an integer
The graph of y   f  x  can be sketched by first drawing y  f  x 
n
and noticing;
 all stationary points must still be stationary points
 all points where the curve cuts the x axis are also stationary points
 if f  x   1 then  f  x   f  x 
n

10. (H)Graphs of the Form y   f  x 
n
where n>1 and an integer
The graph of y   f  x  can be sketched by first drawing y  f  x 
n
and noticing;
 all stationary points must still be stationary points
 all points where the curve cuts the x axis are also stationary points
 if f  x   1 then  f  x   f  x 
n
 if f  x   1 then  f  x   f  x 
n

11. y  f x y   f  x 
2
y
1
x
-1

12. y  f x y   f  x 
2
y
1
x
-1

13. y  f x y   f  x 
2
y
1
x
-1

14. y  f x y   f  x 
2
y
1
x
-1

15. (H)Graphs of the Form y   f  x 
n
where n>1 and an integer
The graph of y   f  x  can be sketched by first drawing y  f  x 
n
and noticing;
 all stationary points must still be stationary points
 all points where the curve cuts the x axis are also stationary points
 if f  x   1 then  f  x   f  x 
n
 if f  x   1 then  f  x   f  x 
n
 if n is even then  f  x   0
n

16. (H)Graphs of the Form y   f  x 
n
where n>1 and an integer
The graph of y   f  x  can be sketched by first drawing y  f  x 
n
and noticing;
 all stationary points must still be stationary points
 all points where the curve cuts the x axis are also stationary points
 if f  x   1 then  f  x   f  x 
n
 if f  x   1 then  f  x   f  x 
n
 if n is even then  f  x   0
n
 if n is odd then  f  x  is the same sign of f  x  for any given value of x
n

17. y  f x y   f  x 
3
y
1
x
-1

18. y  f x y   f  x 
3
y
1
x
-1

19. y  f x y   f  x 
3
y
1
x
-1

20. y  f x y   f  x 
3
y
1
x
-1

21. y  f x y   f  x 
3
y
1
x
-1

22. y  f x y   f  x 
3
y
1
x
-1

23. y  f x y   f  x 
3
y
1
x
-1

24. y  f x y   f  x 
3
y
1
x
-1