Question

Which statement proves that F(x) is an exponential function

A.All values of f(x) are odd
B.The functions of f(x) grows by equal differences over equal intervals
C.All values of f(x) are multiples of three
D.The functions of f(x) grows by equal factors over equal intervals

Answer 1

Option D, stating that f(x) grows by equal factors over equal intervals, conclusively proves that F(x) is an exponential function.

Step-by-step explanation:

The exponential function is characterized by its growth by equal factors over equal intervals, which is a distinctive feature of exponential behavior. This means if you have an exponential function f(x), and you increase your input value x by a constant amount, the output value f(x) will be multiplied by a certain constant factor. This is in contrast to linear functions, which grow by equal differences rather than factors.

Therefore, in response to the given choices, Option D, 'The functions of f(x) grows by equal factors over equal intervals', proves that F(x) is an exponential function, in line with the characteristic exponential growth pattern of equal multiplicative changes over equal intervals.