Question

True or False. If possible kindly explain why so that I can understand it. Thanks much.
1. f(x) = 1^x is not an exponential function.

2. Every exponential function is strictly increasing.

Answer 1

1 false

a^x is exponential, for any positive a.

#2 false, since 1^x is constant.

Answer 2

Most mathematical authorities define an exponential function as

f(x) = a^x, where a is any <b>positive</b> number, a ≠ 1, and x is any real number

so #1 is True

#2, what about y = (1/2)^x
as x increases, y decreases, so False