A. (1, 1) (2, 1/2) (3, 1/3) (4, 1/4)
B. (1, 1) (2, 1/4) (3, 1/9) (4 1/16)
C. (1, 1/2) (2, 1/4) (3, 1/8) (4, 1/16)
D. (1, 1/2) (2, 1/4) (3, 1/6) (4, 1/8)
Answer: The only set of ordered pairs that could be generated by an exponential function is option B.
(1, 1) (2, 1/4) (3, 1/9) (4, 1/16)
Explanation :
An exponential function has the form f(x) = ab^x, where a and b are constants. When we plug in different values of x, we get corresponding values of y, and these pairs of values (x,y) form the ordered pairs of the function.
To determine which set of ordered pairs could be generated by an exponential function, we need to look for a pattern in the y-values as x increases. Specifically, if the ratio of y-values for successive x-values is constant, then the function is exponential.
Let’s examine each set of ordered pairs:
A. (1, 1) (2, 1/2) (3, 1/3) (4, 1/4)
The ratio of y-values for successive x-values is always 1/2, which is not a constant. Therefore, this set of ordered pairs cannot be generated by an exponential function.
B. (1, 1) (2, 1/4) (3, 1/9) (4, 1/16)
The ratio of y-values for successive x-values is always 1/4, which is a constant. Therefore, this set of ordered pairs could be generated by an exponential function.
C. (1, 1/2) (2, 1/4) (3, 1/8) (4, 1/16)
The ratio of y-values for successive x-values is always 1/2, which is not a constant. Therefore, this set of ordered pairs cannot be generated by an exponential function.
D. (1, 1/2) (2, 1/4) (3, 1/6) (4, 1/8)
The ratio of y-values for successive x-values is not constant, so this set of ordered pairs cannot be generated by an exponential function.
Therefore, the correct answer is B: (1, 1) (2, 1/4) (3, 1/9) (4, 1/16).
