Answer:
6. y = 2·2^x — exponential
7. y = (1/16)·4^x — exponential
8. neither
9. neither
Explanation:
First of all, no table with an entry for 0 will be an inverse relation. When the ratio of one term to the next is a constant, the function is exponential. When the difference from one term to the next is a constant, the function is linear.
Here, some tricks are thrown in. The first two (6 and 7) are exponential functions. The common ratios are 2 and 4, respectively. The multiplier is the value of the function when x=0.
6. y = 2·2^x
7. y = (1/16)·4^x
8. The table for function 8 is that of what is known as a harmonic sequence. The denominator increases linearly. It is a kind of an inverse function, but not the kind we normally call an inverse function.
y = 1/(x+1)
9. The function is not obviously linear, inverse, or exponential. The 6 points can always be described by a polynomial of degree n-1, where n is the number of points. The 5th-degree polynomial that fits these points is tedious to find, but can be found to be ...
y = (120 + 103702x - 213975x^2 + 149665x^3 - 42225 x^4 + 4393x^5)/120
Since the function is not of one of the kinds listed, you are under no obligation to write an equation for it.