Answer:
x f(x) g(x)
-2 6 1/9
-1 10 1/3
0 14 1
1 18 3
2 22 9
Step-by-step explanation:
Model for a linear function:
f(x) = ax + b
Using the points (-2, 6) and (0,14), we can find the values of a and b:
6 = -2a + b
14 = 0a + b
b = 14
From the first equation:
6 = -2a + 14
2a = 8
a = 4
So we have that f(x) = 4x + 14
Now we find the values of f(x) for x = -1, x = 1 and x = 2:
f(-1) = -4 + 14 = 10
f(1) = 4 + 14 = 18
f(2) = 8 + 14 = 22
Model for exponencial equation:
g(x) = a*b^x
Using the points (-2, 1/9) and (-1,1/3), we can find the values of a and b:
1/9 = a*b^(-2)
1/3 = a*b^(-1)
Dividing the second equation by the first, we have:
b = (1/3) / (1/9) = 3
From the second equation:
1/3 = a * b^(-1)
1/3 = a * 1/3
a = 1
So we have that:
g(x) = 3^x
Now we find the values of g(x) for x = 0, x = 1 and x = 2:
g(0) = 3^0 = 1
g(1) = 3^1 = 3
g(2) = 3^2 = 9
