 # Which set of ordered pairs could be generated by an exponential function? A. (-1,-1/2), (0, 0),(1,1/2), (2, 1) B. (–1, –1), (0, 0), (1, 1), (2, 8) C. (-1,1/2), (0, 1), (1, 2), (2, 4) D. (–1, 1), (0, 0), (1, 1), (2, 4) Phoebe 2020-10-31 Answered
Which set of ordered pairs could be generated by an exponential function?
A. $\left(-1,-\frac{1}{2}\right)$, (0, 0),$\left(1,\frac{1}{2}\right)$, (2, 1)
B. (–1, –1), (0, 0), (1, 1), (2, 8)
C. $\left(-1,\frac{1}{2}\right)$, (0, 1), (1, 2), (2, 4)
D. (–1, 1), (0, 0), (1, 1), (2, 4)
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An exponential function has the property that the y-values are multiplied by some common factor a when x incresses by 1.
We note that ench set of ordered pairs contains -1, 0, 1, and 2 as x-values, which are increments of 1.
Let us next determine the ratio of each pair of consecutive y-values for each option.
$\frac{0}{-\frac{1}{2}}=0$
$\left(\frac{1}{2}\right)0=$ Does not: exist
$\frac{1}{\frac{1}{2}}=2$
$\frac{0}{-1}=0$
$\frac{1}{0}$= Does not exist
$\frac{8}{1}=8$
$\frac{1}{\frac{1}{2}}=2$
$\frac{2}{1}=2$
$\frac{4}{2}=2$
$\frac{0}{1}=0$
$\frac{1}{0}$=Does no exist
$\frac{4}{1}=4$
We note that the three ratios are only constant for answer option C and thus answer option C could be generated by an exponential function.
C. $\left(-1,\frac{1}{2}\right)$,(0,1),(1,2),(2,4)