Question

What are the domain and range of the function y = a · b^x, where a > 0 and b > 1?Group of answer choicesDomain = all real numbers; range = all positive real numbersDomain = all real numbers; range = all real numbersDomain = all positive real numbers; range = all positive real numbersDomain = all positive real numbers; range = all real numbers

Answer 1

Domain = all positive real numbers;

Range = all positive real numbers

1) As we can see the function below:

`y=ab^x`

since a >0 and b>1 then we can tell that the Domain, i.e. the set of entries of that function can be defined as All positive Real numbers. The definition of a positive number is to be greater than 0.

2) As for the Range, given that a has to be greater than 0 and b greater than 1 this describes an increasing exponential model, like for instance:

`\begin{gathered} y=ab^x \\ y=1\cdot2^x \\ y=2^x \end{gathered}`

So, any exponential model with these characteristics would have a Range greater than 0 as well: f(x) > 0

3) Thus, the answer is:

Domain = all positive real numbers; range = all positive real numbers