Does the table of values below represent a linear function, exponential function, or neither. Explain how you know.

The given function neither represents the linear function nor represents an exponential function.

Step-by-step explanation:

Given the table

x           y

0          2

2          4

4          8

6         16

Linear Function has the following characteristics:

The constant change in x and y

Exponential Function has the following characteristics:

Determining the nature of the function

Given the table

x    0     2      4       6

y     0     4      8       16

Linear Function has the following characteristics:

The constant change in x and y

Checking the constant change in x

i.e. 2-0 = 2, 4-2 = 2, 6-4 = 2

Thus, there is a constant change in x values.

Checking the constant change in y

4-0 = 4, 8-4 = 0, 16-8= 8

Thus, there NO constant change in y values.

Therefore, the given function DOES NOT represent the linear function.

Determining if the given function is Exponential function or not.

CHECKING THE CONSTANT CHANGE IN X VALUE

i.e. 2-0 = 2, 4-2 = 2, 6-4 = 2

Thus, there is a constant change in x values.

Checking the CONSTANT RATIO

4/0=∞, 8/4 = 2, 16/8 = 2

It is clear that there is no constant ratio.

Therefore, the given function DOES NOT represent the exponential function.

Conclusion:

Thus, the given function neither represents the linear function nor represents an exponential function.

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