Question

Narysuj i oblicz funkcje wykladnicza .
Z Góry dziekuje :)
PILNE!

Answer 1

1)
f(x) = (1/2)^(x+1)+1
^ - do potęgi
Obliczenia do tabelki:
f(-3) = (1/2)^(-3+1) + 1= (1/2)^-2 + 1 = 2^2 + 1 = 5
f(-2) = (1/2)^(-2+1) + 1 = (1/2)^-1 + 1 = 2+1 = 3
f(-1) = (1/2)^(-1+1)  +1 = (1/2)^0 + 1 = 2
f(0) = (1/2)^(0+1) + 1 = (1/2)^1 + 1 = 3/2
f(1) = (1/2)^(1+1)+1 = (1/2)^2 + 1 = 1 1/4
f(2) = (1/2)^{2+1) + 1 = (1/2)^3 + 1 = 1 1/8
f(3) = (1/2)^(3+1) + 1 = (1/2)^4 + 1 = 1 1/16
Tabelki są w ostatnim załączniku
Wykres w zał. 1

2)
f(x) = (1/3)^(x-1) - 1
f(-2) = (1/3)^(-2-1)-1 =(1/3)^-3 - 1 = 27 -1 = 26
f(-1) = (1/3)^(-1-1)-1 = (1/3)^(-2) - 1 = 9-1 = 8
f(0) = (1/3)^(0-1)-1 = (1/3)^(-1) - 1 = 3 - 1 = 2
f(1) = (1/3)^(1-1)-1 = (1/3)^(0) - 1 = 1-1 = 0
f(2) = (1/3)^(2-1)-1 = (1/3)^(1) - 1 = 1/3-1 = -2/3
f(3) = (1/3)^(3-1)-1 = (1/3)^(2) - 1 = 1/9 - 1 = -8/9
f(4) = (1/3)^(4-1)-1 = (1/3)^(3) - 1 = 1/27 - 1 = -26/27

Wykres w zał 2

3)
f(x) = 3^(x+1) - 1
f(-4) = 3^(-4+1) - 1 = 3^(-3) - 1 = 1/27 - 1 = -26/27
f(-3) = 3^(-3+1) - 1 = 3^(-2) - 1 = 1/9 - 1 = -8/9
f(-2) = 3^(-2+1) - 1 = 3^(-1) - 1 = 1/3 - 1 = -2/3
f(-1) = 3^(-1+1) - 1 = 3^(0) - 1 =  1 - 1 = 0
f(0) = 3^(0+1) - 1 = 3^(1) - 1 = 3 - 1 = 2
f(1) = 3^(1+1) - 1 = 3^(2) - 1 = 9 -1 = 8
f(2) = 3^(2+1) - 1 = 3^(3) - 1 = 27 - 1 = 26
Wykres w zał 3

4)
f(x)  = 3^(x-1)+1
f(-4) = 3^(-4-1) + 1  = 3^(-5) + 1 = 1/243 +1 = 1 1/243
f(-3) = 3^(-3-1) + 1  = 3^(-4) + 1 =  1/81 + 1 = 1 1/81
f(-2) = 3^(-2-1) + 1  = 3^(-3) + 1 =  1/27 + 1 = 1 1/27
f(-1) = 3^(-1-1) + 1  = 3^(-2) + 1 =  1/9 + 1 = 1 1/9
f(1) = 3^(1-1) + 1  = 3^(0) + 1 = 1 +1 = 2
f(2) = 3^(2-1) + 1  = 3^(1) + 1 = 3+1 = 4
f(3) = 3^(3-1) + 1  = 3^(2) + 1 = 9 +1 = 10
f(4) = 3^(4-1) + 1  = 3^(3) + 1 = 27 +1 = 28
Wykres w zał 4