# Which set of ordered pairs could be generated by an exponential function?

Which set of ordered pairs could be generated by an exponential function? a. (0, 0), (1, 1), (2, 8), (3, 27) b. (0, 1), (1, 2), (2, 5), (3, 10) c. (0, 0), (1, 3), (2, 6), (3, 9) d. (0, 1), (1, 3), (2, 9), (3, 27)
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D All the points go up at the same rate. Every time you add 1 to x, you multiply the y by 3.
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Jeffrey Jordon

The general expression for the exponential function is $f\left(x\right)=a\cdot {b}^{x}$, where .

Note that the graph of each exponential function passes through the point (0,a), because $f\left(x\right)=a\cdot {b}^{0}$ then options A and C are false.

First point in options B and D is (0,1), then

$f\left(0\right)=1⇒a=1$

and you get the expression $f\left(x\right)={b}^{x}$ for the exponential function.

Points (0,1), (1,3), (2,9) and (3,27) represent the powers of 3. In this case $f\left(x\right)={3}^{x}$

Points (0,1), (1,2), (2,5) and (3,10) couldn't generate any exponential function, because if ${b}^{1}=2$ then ${b}^{2}={2}^{2}=4\ne 5$