Final answer:
h(x) = 2^x - 1 is indeed a function as it meets the definition of having a single output for each input. Its domain is all real numbers and its range is all real numbers greater than -1.
Step-by-step explanation:
Is h(x) a Function?
Yes, h(x) = 2x - 1 is a function, because for every value of x in the domain, there is exactly one corresponding value of h(x). This adheres to the definition of a function, which requires each input to have only one output.
Domain of h(x)
The domain of h(x) is all real numbers because we can raise 2 to any real number power. Therefore, the domain is (-∞, ∞) .
Range of h(x)
The range of h(x) is all real numbers greater than -1, because 2x is always positive and subtracting 1 means the smallest value h(x) can take is -1. Therefore, the range is (-1, ∞) .