Complete the following table so that f(x) represents a linear function and g(x)
represents an exponential function,

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

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

the answer to the expression is 83