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Mocninné funkces racionální mocninou
; ;aby x a Z b N
Mocninné funkces racionální mocninou
; ;aby x a Z b N
3) 0 1a
b2) 1 0
a
b1) 1
a
b4) 1
a
b
Mocninné funkces racionální mocninou
; ;aby x a Z b N
3) 0 1a
b2) 1 0
a
b1) 1
a
b4) 1
a
b
a sudéb liché
a lichéb sudé
a lichéb liché
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a lichéb sudé
5
4554 4
1 1y x
x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a lichéb sudé
5
4554 4
1 1y x
x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a lichéb sudé
5
4554 4
1 1y x
x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a sudéb liché
a lichéb sudé
8
383 8 3
1 1y x
x x
5
4554 4
1 1y x
x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a sudéb liché
a lichéb sudé
8
383 8 3
1 1y x
x x
5
4554 4
1 1y x
x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a sudéb liché
a lichéb sudé
8
383 8 3
1 1y x
x x
5
4554 4
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
8
383 8 3
1 1y x
x x
5
4554 4
1 1y x
x x
5
353 5 3
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
8
383 8 3
1 1y x
x x
5
4554 4
1 1y x
x x
5
353 5 3
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
8
383 8 3
1 1y x
x x
5
4554 4
1 1y x
x x
5
353 5 3
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
3
1lichá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
1) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
8
383 8 3
1 1y x
x x
5
4554 4
1 1y x
x x
5
353 5 3
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
3
1lichá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a lichéb sudé
3
4334 4
1 1y x
x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a lichéb sudé
3
4334 4
1 1y x
x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a lichéb sudé
3
4334 4
1 1y x
x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
a lichéb liché
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
3
535 3 5
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
a lichéb liché
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
3
535 3 5
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
a lichéb liché
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
3
535 3 5
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
3
1lichá- typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
a lichéb liché
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
3
535 3 5
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
3
1lichá- typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
2) 1 0a
b
a sudéb liché
a lichéb sudé
a lichéb liché
2
727 2 7
1 1y x
x x
3
4334 4
1 1y x
x x
3
535 3 5
1 1y x
x x
1 ani sudá ani licháf
2 2
1sudá - typ " "f
x
3
1lichá- typ " "f
x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a lichéb sudé
33
34 44y x x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a lichéb sudé
33
34 44y x x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a lichéb sudé
33
34 44y x x x
1 ani sudá ani lichá - typ " "f x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a sudéb liché
a lichéb sudé
22
7 2 77y x x x
33
34 44y x x x
1 ani sudá ani lichá - typ " "f x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a sudéb liché
a lichéb sudé
22
7 2 77y x x x
33
34 44y x x x
1 ani sudá ani lichá - typ " "f x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a sudéb liché
a lichéb sudé
22
7 2 77y x x x
33
34 44y x x x
1 ani sudá ani lichá - typ " "f x
2 sudá - 1. a 2.kvadrant!!f
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
22
7 2 77y x x x
33
34 44y x x x
33
5 3 55y x x x
1 ani sudá ani lichá - typ " "f x
2 sudá - 1. a 2.kvadrant!!f
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
22
7 2 77y x x x
33
34 44y x x x
33
5 3 55y x x x
1 ani sudá ani lichá - typ " "f x
2 sudá - 1. a 2.kvadrant!!f
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
22
7 2 77y x x x
33
34 44y x x x
33
5 3 55y x x x
1 ani sudá ani lichá - typ " "f x
2 sudá - 1. a 2.kvadrant!!f
3
3 lichá - typ " "f x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
3) 0 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
22
7 2 77y x x x
33
34 44y x x x
33
5 3 55y x x x
1 ani sudá ani lichá - typ " "f x
2 sudá - 1. a 2.kvadrant!!f
3
3 lichá - typ " "f x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a lichéb sudé
55
54 44y x x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a lichéb sudé
55
54 44y x x x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a lichéb sudé
55
54 44y x x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a sudéb liché
a lichéb sudé
88
3 8 33y x x x
55
54 44y x x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a sudéb liché
a lichéb sudé
88
3 8 33y x x x
55
54 44y x x x
1 ani sudá ani licháf Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a sudéb liché
a lichéb sudé
88
3 8 33y x x x
55
54 44y x x x
1 ani sudá ani licháf
2
2 sudá - typ " "f x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
88
3 8 33y x x x
55
54 44y x x x
55
3 5 33y x x x
1 ani sudá ani licháf
2
2 sudá - typ " "f x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
88
3 8 33y x x x
55
54 44y x x x
55
3 5 33y x x x
1 ani sudá ani licháf
2
2 sudá - typ " "f x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
88
3 8 33y x x x
55
54 44y x x x
55
3 5 33y x x x
1 ani sudá ani licháf
2
2 sudá - typ " "f x
3
3 lichá - typ " "f x
Jen 1.kvadrant
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
4) 1a
b
a sudéb liché
a lichéb sudé
a lichéb liché
88
3 8 33y x x x
55
54 44y x x x
55
3 5 33y x x x
1 ani sudá ani licháf
2
2 sudá - typ " "f x
3
3 lichá - typ " "f x
Jen 1.kvadrant
Shrnutí aby x
Shrnutí aby x
a sudéb liché
a lichéb sudé
a lichéb liché
Shrnutí aby x
0a
b0 1
a
b1
a
b
a sudéb liché
a lichéb sudé
a lichéb liché
Shrnutí aby x
0a
b0 1
a
b1
a
b
a sudéb liché
a lichéb sudé
a lichéb liché 9
Shrnutí aby x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
0a
b0 1
a
b1
a
b
a sudéb liché
a lichéb sudé
a lichéb liché 9
0a
b
Shrnutí aby x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
-1.5
-1
-0.5
0.5
1
1.5
2
x
y
0a
b0 1
a
b1
a
b
a sudéb liché
a lichéb sudé
a lichéb liché 9
0a
b 0 1a
b
Shrnutí aby x
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
-1.5
-1
-0.5
0.5
1
1.5
2
x
y
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-4
-3
-2
-1
1
2
3
4
x
y
0a
b0 1
a
b1
a
b
a sudéb liché
a lichéb sudé
a lichéb liché 9
0a
b 0 1a
b1
a
b
KONEC
