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

Answered question

2021-06-22

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)

Answer & Explanation

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.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-20Added 2605 answers

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

Keep in mind that each exponential function's graph goes past 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) was unable to produce any exponential functions because  b1=2 then b2=22=45

So, D is correct answer

 

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