Determine the type of function each table represents. Write “linear”, “exponential”, or “neither”. Two-way table with x-values 0, 1, 2, 3, 4 and y-values 0, 1, 4, 9, 16
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Two-way table with x-values 0, 1, 2, 3, 4 and y-values 1/3, 1, 3, 9, 27
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Two-way table with x-values 0, 1, 2, 3, 4 and y-values 5, 5/2, 5/4, 5/8, 5/16
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Two-way table with x-values 0, 1, 2, 3, 4 and y-values 4.5, 4, 3.5, 3, 2.5
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1) Neither

2) Exponential

3) Exponential

4) Linear

Step-by-step explanation:

1) x-values       y-values

0                          0

1                           1

2                          4

3                           9

4                          16

Therefore, we have, the relationship of the function given as_f(x) = x² Which is neither a linear function nor an exponential function

2) x-values       y-values

0                          1/3

1                           1

2                          3

3                           9

4                          27

The relationship between 'x', and 'y' is given as follows;

f(x) = 3⁽ˣ⁻¹⁾

Therefore, the relationship between 'x', and 'y', is an exponential relationship, and the function is an exponential function

3) x-values       y-values

0                           5

1                           5/2

2                          5/4

3                           5/8

4                          5/16

The relationship between 'x', and 'y' is given as follows;

f(x) = 5×(1/2)ˣ

Therefore, the relationship between 'x', and 'y', is an exponential relationship, and the function is an exponential function

4) x-values       y-values

0                           4.5

1                           4

2                          3.5

3                           3

4                          2.5

The given data for the y-values has a constant first common difference of 4 - 4.5 = -0.5, therefore, the relationship between the 'x', and 'y' values is a linear relationship.