|
24. Chiziqli funksiya
–
y = kx + b
ko‘rinishdagi funksiya, bunda
k
va
b
– berilgan sonlar.
y = kx + b
chiziqli funksiyaning grafigi – to‘g‘ri chiziq,
b
= 0
bo‘lganda funksiya
y = kx
ko‘rinishni oladi, uning grafigi koordinatalar
boshidan o‘tadi.
25. Òo‘g‘ri proporsional bog‘lanish
–
y = kx
formula bilan ifoda-
langan bog‘lanish, bunda
k >
0,
x
> 0.
26. Òeskari proporsional bog‘lanish
, bu
k
x
y
=
formula bilan ifoda-
langan bog‘lanish, bunda
k
> 0,
x
> 0,
k
– proporsionallik koeffitsiyenti.
k
x
y
=
(
k
¹
0) funksiya
x
¹
0 bo‘lganda aniqlangan, noldan boshqa
barcha haqiqiy qiymatlarni qabul qiladi.
Agar
k
> 0 bo‘lsa, u holda
k
x
y
=
funksiya (masalan,
x
x
y
y
2
1
2
,
=
=
):
a)
x
> 0 bo‘lganda musbat qiymatlarni,
x
< 0 bo‘lganda manfiy
qiymatlarni qabul qiladi:
b)
x
< 0 va
x
> 0 oraliqlarda kamayadi.
Agar
k
< 0 bo‘lsa,
k
x
y
–
=
funksiya (masalan,
x
y
1
–
=
,
x
y
=
2
– ,
x
y
=
1
3
–
)
a)
x
< 0 bo‘lganda musbat qiymatlarni va
x
> 0 bo‘lganda manfiy
qiymatlarni qabul qiladi;
b)
x
< 0 va
x
> 0 oraliqlarda o‘sadi.
k
x
y
=
funksiyaning grafigi
giperbola
deyiladi. U koordinatalar
boshiga nisbatan simmetrik joylashgan ikkita tarmoqqa ega.
k
> 0
bo‘lganda grafik birinchi va uchinchi choraklarda,
k
< 0 bo‘lganda esa
ikkinchi va to‘rtinchi choraklarda joylashadi.
225
JAVOBLAR
2.
2)
x
1
=
0,
x
2
=1; 4)
x
ning berilgan funksiyaning qiymati –5 ga teng bo‘ladigan
haqiqiy qiymatlari yo‘q.
3.
2)
1
3
4
1
x
=
,
x
2
= –1; 4)
x
1
= 0,
2
3
4
x
=
.
4.
2) 0; 4) 1.
5.
2) nollari yo‘q; 4)
1
2
3
x
=
,
2
1
2
x
=
; 6) nollari yo‘q; 8)
x
= 1.
6.
2)
p
= 3,
q
= –4;
4)
p
= –2,
q
= –15.
7.
x
1,2
= ±2.
9.
B
va
C
.
12.
2) ( 5 ; 5), (– 5 ; 5); 4) (0; 0),
(2; 4); 6) (1; 1).
13.
2) Ha.
14.
2) Ha; 4) yo‘q;
16.
1)
x
< –3,
x
> 3; 2) –5
£
x
£
5;
3)
x
£
–4,
x
³
4; 4) –6 <
x
< 6.
20.
2) (–3; –4,5), (2; –2).
21.
2) Ha; 4) yo‘q.
22.
1) O‘suvchi; 2) kamayuvchi; 3) o‘suvchi; 4) o‘suvchi ham, kamayuvchi ham
bo‘lmaydi.
23.
3 m/s
2
.
26.
2) (0; –5); 4)
1 1
;
8 16
æ
ö
ç
÷
è
ø
.
27.
2)
x
= –2; 4)
x
= 2;
6)
3
4
x
=
.
28.
2) Yo‘q; 4) yo‘q.
29.
2) (1; 0), (0,5; 0), (0; –1); 4) (0; 0),
4
3
; 0
æ
ö
ç
÷
è
ø
.
30.
y
=
x
2
– 2
x
+ 3.
32.
2)
k
= –10.
34
. 1)
y
= 2(
x
– 3)
2
; 2)
y
= 2
x
2
+ 4;
3)
y
= 2(
x
+ 2)
2
– 1; 4)
y
= 2(
x
– 1,5)
2
+ 3,5.
35.
2)
3 11
;
2 4
æ
ö
-
ç
÷
è
ø
; 4)
5 21
;
2 4
æ
ö
ç
÷
è
ø
.
36.
2) (1; 0), (–5; 0), (0; 10); 4) (0; 14).
40.
7,5+7,5.
41.
5 va 5.
42.
Devorga
parallel tomon 6 m; qolgan tomonlari 3 m dan.
43.
Yo‘q.
44.
2)
x
= 1 da
y
= –5
eng kichik qiymat; 4)
x
= 1 da
y
= –2 eng kichik qiymat.
45.
1)
a
> 0,
b
> 0,
c
> 0; 2)
a
< 0,
b
> 0,
c
< 0.
46.
1) 5 s dan keyin eng katta balandlik 130
m ga teng; 2)
(5
26)
s
+
.
47.
2)
x
1
= 2,
x
2
= 0,5; 4)
x
ning bunday qiymati
yo‘q.
48.
2) (1; 1), (2; 4); 4) (–5; 18).
49.
2)
x
< –6,
x
> 6.
50.
2) (5; 0),
(–2; 0) , (0; 10); 4) (1; 0),
11
;
7
0
æ
ö
-
ç
÷
è
ø
, (0; –11).
51.
2) (–1; 4); 4)
1
;
2
1
æ
ö
ç
÷
è
ø
-
;
6)
1
1
;
2
4
6
æ
ö
ç
÷
è
ø
- -
.
53.
2) Eng katta qiymat 4 ga teng; 4) eng kichik qiymat
2
3
3 ga
teng.
54.
150 m va 150 m.
55.
200 m va 400 m.
56.
2)
p
= 1,
q
= 0.
57.
2)
p
= –4,
q
= 3.
58.
1)
x
1
= 1,
x
2
= –5; 2)
x
1
= 0,
x
2
= 1,
x
3
= 2.
59.
1)
a
= 1,
b
= –2,
c
= 0;
2)
a
= 1,
b
= –2,
c
= 4; 3)
a
= –2,
b
= 8,
c
= –6.
61.
2) 3
x
2
–
x
– 1 > 0;
4) 2
x
2
+
x
– 5 < 0.
63.
2) 3
< x
< 11; 4)
x < –
7,
x
> –1.
64.
2)
x < –
3,
x
> 3;
4)
x
< 0,
x
> 2.
65.
2) –2
< x
< 1; 4)
x < –
3,
x
> 1; 6)
x < –
1,
x
>
1
3
.
66.
2)
x
=
1
6
; 4)
x
< –4,
x
> 2.
69.
Musbat qiymatlar
x
< –3,
x
> 2 oraliqlarda,
15 – Algebra, 9- sinf uchun
226
manfiy qiymatlar –3 <
x
< 2 intervalda.
71.
2)
x
£
–1,
x
³
4; 4) –1 <
x
< 4.
72.
2)
x
<
1
3
-
,
x
> 2; 4)
x
£
–0,25;
x
³
1.
73
. 2)
x
= 7; 4) yechimlari yo‘q;
6)
x
– istalgan haqiqiy son.
74.
2) Yechimlari yo‘q; 4) yechimlari yo‘q; 6)
x
–
istalgan haqiqiy son.
75.
2)
x
<
7
-
,
x
> 7 ; 4)
x
< –2;
x
> 0; 6)
x
< –5;
x
> 3;
8) –2 <
x
< 1.
77.
2)
x
<
5
3
-
,
x
>
5
3
; 4) –1 <
x
< 4; 6)
x
– istalgan haqiqiy son;
8)
x
= –3.
78.
2)
x
– istalgan haqiqiy son; 4)
x
¹
1
4
; 6)
1
3
-
£
x
£
0; 8) yechim-
lari yo‘q.
79.
2) Yechimlari yo‘q; 4) –0,5 <
x
< 3; 6)
x
– istalgan haqiqiy son.
80.
2)
x
= 1; 4)
x
– istalgan haqiqiy son.
82.
–6 <
r
< 2.
84.
2) –5 <
x
< 8;
4)
x
< –5,
x
>
1
2
3 .
85.
2)
x
< 0,
x
> 9; 4) –3 <
x
< 0; 6)
x
< –1,
x
> 3.
86.
2) –
1
2
<
x
< 0,
x
>
1
2
; 4) –2 <
x
< 2,
x
> 5.
87.
2) –7 <
x
< 7; 4) –4 <
x
< 4,
x
> 4; 6)
x
= –2; 2
£
x
£
5.
88.
2) –3 <
x
< 4; 4) –3,5
£
x
< 7; 6) –2
£
x
< –1,
x
³
3.
89.
2)
x
< 0,5,
x
> 1; 4)
x
< –
2
3
, 0 <
x
<
1
2
,
x
>
2
3
.
90
. 2) –4 <
x
< –2,
x
> 3; 4) –3
£
x
£
–1, 4
£
x
£
5.
91.
2)
x
< –2, 2 <
x
< 6; 4)
x
< –3, –1
£
x
< 2,
x
³
4.
92.
2)
15
-
<
x
<
–3, 0 <
x
< 15 .
93.
1) –8 <
x
< –1; 2)
x
< –5,
x
> 2;
3) –1 <
x
£
–
2
5
; 4)
x
< –4, –4 <
x
<
3
2
,
x
> 4.
94.
2)
x
< 2,
x
> 4; 4)
x
< 3,
x
> 4.
95.
2)
x
< –6,
x
> 6; 4) –
3
4
£
x
£
3
4
.
96.
2) –
1
2
£
x
£
1
2
; 4)
x
£
0,
x
³
1
3
97.
2)
x
<
1
2
,
x
> 4; 4) –2 <
x
<
1
2
; 6)
x
<
4
5
,
x
> 1.
98.
2)
x
¹
–5; 2)
x
¹
–
3
2
; 6)
x
¹
1
2
.
99.
2)
Yechimlari yo‘q; 4) yechimlari yo‘q; 6) yechimlari yo‘q.
100.
2)
x
< –1, 1 <
x
< 4; 4)
x
< –
1
2
, 4 <
x
£
7; 6)
x
³ 2,
–
1
2
£
x
<
1.
101.
2) –1 <
x
<
5; 4) –5
£
x
£
2; 6)
x
£
3
2
,
x
³
1
3
.
102.
2)
x
– istalgan haqiqiy son; 4) yechimlari yo‘q; 6)
1
2
<
x
<
1; 8)
x
–
istalgan haqiqiy son.
103.
2)
x
£
3
–
2
,
x
³
–1; 4)
x
=
2
3
; 6) yechimlari yo‘q.
104.
2)
x
<
3
-
;
3
2
-
<
x
<
3 ; 4) x < –4, –1 <
x
£
1,
x
> 1.
105.
2) –1 <
x
<
1
5
-
,
3
4
<
x
< 2;
4) –
1
3
<
x
£
1
5
-
,
1
2
<
x
£
2.
106.
12 km/soatdan kam emas.
108.
2)
x
< –3, –2 <
x
< 1,
x
³
3; 2) –3 <
x
< –2, –1
£
x
£
1; 3) – 2
<
x
<
–1, 1
<
x
<
2 ; 4)
x
< –2,
3
-
<
x
< –3,
x
> 2.
109.
2) 32; 4) 0.
110.
2)
( )
5
1
5
; 4)
( )
2
c
d
.
112.
2) 21
–3
; 4)
a
–9
.
113.
2)
121
81
;
227
4) 32; 6)
1
169
-
.
114.
2)
53
16
; 4) –875.
116.
2)
3
1
(
)
x y
+
; 4)
3
4
9
a
b
; 6)
2
4
a
bc
.
117.
2) –125;
4)
1
17
.
118.
2) 0,0016; 4)
16
625
.
119.
2)
b
8
; 4)
b
–28
.
120.
2)
a
8
b
–4
; 4) 3
–4
a
–12
;
121.
2)
m
12
n
–15
; 4) –64
x
–15
y
3
z
–9
.
122.
2)
97
9
-
.
123.
2) 2,7
∙
10
–8
; 4) 8
∙
10
–9
.
124.
2) 5,086
∙
10
–8
; 4) 1,6
∙
10
–3
.
125.
0,003.
126.
10
–11
.
127.
0,0001 mm.
128.
2)
a
5
,
1
32
.
129.
2) 0.
130.
2)
b
–
a
.
132.
2) 2; 4) 15.
133.
2) 81; 4)
1
81
.
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