which set of ordered pairs could be generated by an exponential function? (0, 0), (1, 1), (2, 8), (3, 27)…

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is (y = a\cdot b^{x}), where (a\neq0), (b> 0) and (b\neq1). When (x = 0), (y=a\cdot b^{0}=a). So, for an exponential function, when (x = 0), (y\neq0) (since (a\neq0)). This eliminates the sets ((0,0),(1,1),(2,8),(3,27)) and ((0,0),(1,3),(2,6),(3,9)).

Step2: Check the ratio of (y) - values for remaining sets

For an exponential function (y = a\cdot b^{x}), the ratio of (y) - values for consecutive integer values of (x) is constant. Consider the set ((0,1),(1,2),(2,5),(3,10)). The ratios are (\frac{2}{1}=2), (\frac{5}{2}=2.5), (\frac{10}{5}=2). The ratios are not constant. Consider the set ((0,1),(1,3),(2,9),(3,27)). The ratios are (\frac{3}{1}=3), (\frac{9}{3}=3), (\frac{27}{9}=3). The ratio of (y) - values for consecutive integer values of (x) is constant ((b = 3) and (a = 1), and the function is (y=3^{x})).

Answer:

((0,1),(1,3),(2,9),(3,27))