1. (I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;

2. (I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;
 f  x  is only defined if f  x   0

3. y  f x
y
1
x
-1

4. y  f x
y
1
x
-1

5. (I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;
 f  x  is only defined if f  x   0
 f  x   0 for all x in the domain

6. (I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;
 f  x  is only defined if f  x   0
 f  x   0 for all x in the domain
 f  x   f  x  if f  x   1 and f  x   f  x  if f  x   1

7. y  f x
y
1
x
-1

8. y  f x
y
1
x
-1

9. y  f x
y
1
x
-1

10. (I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;
 f  x  is only defined if f  x   0
 f  x   0 for all x in the domain
 f  x   f  x  if f  x   1 and f  x   f  x  if f  x   1
dy f  x 
  implies;
dx f x

11. (I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;
 f  x  is only defined if f  x   0
 f  x   0 for all x in the domain
 f  x   f  x  if f  x   1 and f  x   f  x  if f  x   1
dy f  x 
  implies;
dx f x
 stationary points must still be stationary points

12. (I)Graphs of the Form y  f  x
The graph of y  f  x  can be sketched by first drawing y  f  x 
and noticing;
 f  x  is only defined if f  x   0
 f  x   0 for all x in the domain
 f  x   f  x  if f  x   1 and f  x   f  x  if f  x   1
dy f  x 
  implies;
dx f x
 stationary points must still be stationary points
 there are critical points where f  x   0

13. y  f x
y
y f x
1
x
-1

14. y  f x
y
y f x
1
x
-1

15. y  f x
y
y f x
1
x
-1

16. y
1
y 2  f x
x
-1

17. y
1
y 2  f x
x
-1

18. y
1
y 2  f x
x
-1