1. Regions In The Plane
To draw a region, first you have to sketch the curve.

2. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line

3. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line
2) If  or  use a solid line

4. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line
2) If  or  use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)

5. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line
2) If  or  use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.

6. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line
2) If  or  use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.
e.g. (i ) y  x  3

7. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line
2) If  or  use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.
e.g. (i ) y  x  3
y y  x3
3
–3 x

8. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line
2) If  or  use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.
e.g. (i ) y  x  3
y y  x3
test (0,0)
03 3
–3 x

9. Regions In The Plane
To draw a region, first you have to sketch the curve.
1) If < or > use a dotted line
2) If  or  use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.
e.g. (i ) y  x  3
y y  x3
test (0,0)
03 3
–3 x

10. (ii ) x 2  y 2  9

11. (ii ) x 2  y 2  9 y
3
x2  y 2  9
–3 3 x
–3

12. (ii ) x 2  y 2  9 y
test (0,0)
3
02  02  9 x2  y 2  9
09
–3 3 x
–3

13. (ii ) x 2  y 2  9 y
test (0,0)
3
02  02  9 x2  y 2  9
09
–3 3 x
–3

14. (ii ) y  4  x 2

15. (ii ) y  4  x 2 y
2 y  4  x2
–2 2 x

16. (ii ) y  4  x 2 y
test (0,0)
0  40 2 2 y  4  x2
02
–2 2 x

17. (ii ) y  4  x 2 y
test (0,0)
0  40 2 2 y  4  x2
02
–2 2 x

18. (ii ) y  4  x 2 y
test (0,0)
0  40 2 2 y  4  x2
02
–2 2 x

19. (iv) y  x 2 and y  3 x  4

20. (iv) y  x 2 and y  3 x  4 y
y  x2
x

21. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2
test (0,1)
0  12
0 1
x

22. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2
test (0,1)
0  12
0 1
x

23. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2
test (0,1) y  3x  4
0  12
0 1
x

24. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2 y  3x  4
test (0,1) test (0,0) y  3x  4
0  12 0 04
0 1 04
x

25. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2 y  3x  4
test (0,1) test (0,0) y  3x  4
0  12 0 04
0 1 04
x

26. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2 y  3x  4
test (0,1) test (0,0) y  3x  4
0  12 0 04
0 1 04
point of intersection x
x 2  3x  4

27. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2 y  3x  4
test (0,1) test (0,0) y  3x  4
0  12 0 04
0 1 04
point of intersection x
x 2  3x  4
x 2  3x  4  0
 x  1 x  4   0
x  1 or x  4

28. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2 y  3x  4
test (0,1) test (0,0) y  3x  4
0  12 0 04 (4,16)
0 1 04 (1,1)
point of intersection x
x 2  3x  4
x 2  3x  4  0
 x  1 x  4   0
x  1 or x  4

29. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2 y  3x  4
test (0,1) test (0,0) y  3x  4
0  12 0 04 (4,16)
0 1 04 (1,1)
point of intersection x
x 2  3x  4
x 2  3x  4  0
 x  1 x  4   0
x  1 or x  4
Exercise 3F; 3ac, 4d, 5cg, 6cd, 7, 10, 12a, 15a, 19, 20, 21a, 23*

30. (iv) y  x 2 and y  3 x  4 y
y  x2
y  x2 y  3x  4
test (0,1) test (0,0) y  3x  4
0  12 0 04 (4,16)
0 1 04 (1,1)
point of intersection x
x 2  3x  4
x 2  3x  4  0
 x  1 x  4   0
x  1 or x  4