What are the domain and range of the exponential function f(x)=ab^x where b is a positive real number not equal to 1 and a> 0?

For this case we have a function of the form:

Where

The domain of that function is given by all the values that x can take.

If b is a positive real number other than 1 and a> 0, we have that the domain of f (x) is given by (-∞,∞). x can take any value.

On the other hand, the range is given by the dependent values of the variable "y".

IF we evaluate f (-∞) then y tends to zero.

If we evaluate f (∞) then y tends to infinity.

Thus, the range is: (0, ∞)

So, we have:

Domain: (-∞,∞)

Range: (0, ∞)

Option C