Graph each system of inequalities. See Examples 4 – 6.
- 4 x+ 3 y 712
3 x- y7- 6
x- 2 y 64
2 x+ 5 y 610
23. 24.
x+ y... 5
4 x- 3 y... 0
4 x+ yÚ 4
5 x- 3 y... 15
25. 26.
y... 4
xÚ- 2
y... 4
x... 5
27. 28.
x^2
16
+
y^2
9
... 1
x^2 - y^2 Ú 9
y6-x^2 + 3
y 7 x^2 - 4
For each nonlinear inequality in Exercises 33 – 40, a restric-
tion is placed on one or both variables. For example, the
inequality
is graphed in the figure. Only the right half of the interior of
the circle and its boundary is shaded, because of the restric-
tion that x must be nonnegative. Graph each nonlinear in-
equality with the given restrictions.
- , 34. ,
- , 36. ,
- , 38. ,
39.x^2 + 4 y^2 Ú 1 ,, xÚ 0 yÚ 0 40. 2 x^2 - 32 y^2 ... 8 ,, x... 0 yÚ 0
4 x^2 - y^2716 x 60 x^2 +y^274 y 60
x 6 y^2 - 3 x 60 x^2 - y^264 x 60
x^2 +y^2736 xÚ 0 4 x^2 + 25 y^26100 y 60
x^2 +y^2 ...4, xÚ 0
x
y
0
2
2
x^2 + y^2 Ä 4, x ê 0
41. 42.
y...x^2 - 3
yÚ-x^2 + 5
y...-x+ 4
yÚx- 3
43. 44.
y 65
y 71 x- 422 - 3
y7- 3
y 6 x^2 + 4 x+ 4
Evaluate each expression for (a) ( b) (c) and (d) See
Section 1.3.
- 47.n 2 - n 48.n 1 n- 32
n- 1
n+ 1
n+ 5
n
n=1, n=2, n=3, n=4.
PREVIEW EXERCISES
29. 30.
y^2 - x^2 Ú 4
yÚ 0
xÚ 0
x+y... 5
x^2 +y^2 Ú 4
31. 32.
3 x- 2 y7- 6
x+y 63
y7- 2
y 6 x^2
x 61
y...- 1
yÚx- 3
y...-x^2
Use the shading feature of a graphing calculator to graph each system.
668 CHAPTER 11 Nonlinear Functions, Conic Sections, and Nonlinear Systems
