For power functions, how do you know the domain? How do you it is all non negative number for domain?

Answer 1

For power functions, such as f(x) = a^x (for some constant a), the domain is actually all real numbers.

The range, however, would be (0, infinity), i.e. all positive real numbers.

How does one know this, you ask? It's just the behaviour of the power function; that's all. It is a given fact that power functions in the form f(x) = a^x has a horizontal asymptote of y = 0.

Answer 2

Two questions:

1. What exactly do you mean by 'power function'
and
2. Are you restricted to real numbers?

Answer 3

D = R+ ==> only positive numbers.
D = R- ==> only negative numbers
D = R* ==> all numbers except zero
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