From the table below, determine whether the data shows an exponential function. explain why or why not.
x: 3, 1, -1, -3
y: 1, 2, 3, 4
(a) no; the domain values are at regular intervals and the range values have a common sum 1.
(b) no; the domain values are not at regular intervals.
(c) yes; the domain values are at regular intervals and the range values have a common factor 2.
(d) yes; the domain values are at regular intervals and the range values have a common sum 1.

X        Δx                                   y             Δy

3                                               1          

1        1 - 3 = - 2                        2             2 - 1 = 1

-1        -1 - 1 = -2                      3              3 - 2 = 1

-3        -3 - (-1) = -2                  4               4 - 3 = 1

So, as you see y in increasing in regular constant intervals, when x also increases in regular constant intervals. => Δy / Δx = constant.

That is the result of a linear function, not an exponential one.

So, the true statement is given by the option (A) No; the domain values are at regular intervals and the range values have a common sum 1.

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