Question

Why is b ≠ 1 a condition for f(x) = ab^x?

Answer 1

Explanation:

In this case, we hace the following exponential function:

$f(x)=ab^x$

Where:

$a:Initial \ value \\ \\ b:the \ base$

The base $b\neq 1$ because 1 raised to any power leads the result of 1. That is:

$1^2=1 \\ \\ 1^3=1 \\ \\ 1^{\sqrt{3}}=1 \\ \\ \\ In \ conclusion: \\ \\ 1^{n}=1, \ \text{n any real number}$

If so, then we won't get an exponential function, but a constant function:

$f(x)=a$