Find the Domain and Range y=2^x

Problem

y=2

Solution

1. Identify the type of function. The expression y=2 is an exponential function with a base of 2 and an exponent of x

2. Determine the domain. For any exponential function of the form bx where b>0 the exponent x can be any real number. There are no restrictions such as division by zero or square roots of negative numbers.

3. Determine the range. Since the base 2 is positive, any power of 2 will always result in a value greater than zero. As x approaches negative infinity, y approaches 0 but never reaches it. As x approaches positive infinity, y grows without bound.

Final Answer

Domain: *(−∞,∞), Range: *(0,∞)

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