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

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = ab^{x}$, where $a\neq0$, $b>0$ and $b\neq1$. When $x = 0$, $y=ab^{0}=a$. So, for an exponential function, when $x = 0$, $y=a\neq0$ (except in some degenerate cases which are not the standard form). We can eliminate the options with $(0,0)$.

Step2: Check the ratio of $y$ - values

For an exponential function $y = ab^{x}$, if we have two points $(x_1,y_1)$ and $(x_2,y_2)$, then $\frac{y_2}{y_1}=\frac{ab^{x_2}}{ab^{x_1}}=b^{x_2 - x_1}$. For the set of points $(0,1),(1,3),(2,9),(3,27)$: When $x_1 = 0,y_1 = 1$ and $x_2 = 1,y_2 = 3$, $\frac{y_2}{y_1}=\frac{3}{1}=3$. When $x_1 = 1,y_1 = 3$ and $x_2 = 2,y_2 = 9$, $\frac{y_2}{y_1}=\frac{9}{3}=3$. When $x_1 = 2,y_1 = 9$ and $x_2 = 3,y_2 = 27$, $\frac{y_2}{y_1}=\frac{27}{9}=3$. The ratio of consecutive $y$ - values is constant, which is a characteristic of an exponential function.

Answer:

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