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