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

2021-06-22 Answered
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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Answers (2)

Answered 2021-10-18
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
Answered 2021-10-20 Author has 2313 answers

The general expression for the exponential function is f(x)=abx, where ab, b>0, b1.

Note that the graph of each exponential function passes through the point (0,a), because f(x)=ab0 then options A and C are false.

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

 f(0)=1a=1

and you get the expression f(x)=bx for the exponential function.

Points (0,1), (1,3), (2,9) and (3,27) represent the powers of 3. In this case f(x)=3x

Points (0,1), (1,2), (2,5) and (3,10) couldn't generate any exponential function, because if b1=2 then b2=22=45

Answer: correct choice is D

 

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