Which set of ordered pairs could be generated by an exponential function? A. (−1,−12), (0, 0),(1,12), (2, 1) B. (–1, –1), (0, 0), (1, 1), (2, 8) C. (−1,12), (0, 1), (1, 2), (2, 4) D. (–1, 1), (0, 0), (1, 1), (2, 4)

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. Answer option A 0−12=0 (12)0= Does not: exist 112=2 Answer option B 0−1=0 10= Does not exist 81=8 Answer option C 112=2 21=2 42=2 Answer option Does 01=0 10=Does no exist 41=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. (−1,12),(0,1),(1,2),(2,4)

Resolved: "Which set of ordered pairs could be generated..."

Phoebe

Answered question

2020-10-31

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

(- 1, - \frac{1}{2})

, (0, 0),

(1, \frac{1}{2})

, (2, 1)
B. (–1, –1), (0, 0), (1, 1), (2, 8)
C.

(- 1, \frac{1}{2})

, (0, 1), (1, 2), (2, 4)
D. (–1, 1), (0, 0), (1, 1), (2, 4)

Answer & Explanation

hesgidiauE

Skilled2020-11-01Added 106 answers

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.
Answer option A
$\frac{0}{- \frac{1}{2}} = 0$
$(\frac{1}{2}) 0 =$ Does not: exist
$\frac{1}{\frac{1}{2}} = 2$
Answer option B
$\frac{0}{- 1} = 0$
$\frac{1}{0}$ = Does not exist
$\frac{8}{1} = 8$
Answer option C
$\frac{1}{\frac{1}{2}} = 2$
$\frac{2}{1} = 2$
$\frac{4}{2} = 2$
Answer option Does
$\frac{0}{1} = 0$
$\frac{1}{0}$ =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. $(- 1, \frac{1}{2})$ ,(0,1),(1,2),(2,4)

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