Find the Range y=e^x

Problem

y=ex

Solution

1. Identify the parent function as the natural exponential function, where the base e is approximately 2.718

2. Analyze the behavior of the function as x approaches negative infinity. As x→−∞ ex approaches 0 but never actually reaches it, meaning there is a horizontal asymptote at y=0

3. Analyze the behavior of the function as x approaches positive infinity. As x→∞ ex grows without bound toward ∞

4. Determine the set of all possible output values (y based on the fact that ex is always strictly positive for any real input x

Final Answer

Range:(0,∞)

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