Find the Domain and Range -e^x

Problem

ƒ(x)=−ex

Solution

1. Identify the type of function. The function ƒ(x)=−ex is an exponential function multiplied by a negative constant.

2. Determine the domain. Exponential functions of the form ex are defined for all real numbers because there are no restrictions such as division by zero or square roots of negative numbers.

3. Analyze the range. The basic exponential function ex is always strictly greater than zero for all real x

4. Apply the transformation. Multiplying ex by −1 reflects the graph across the xaxis, changing the outputs from (0,∞) to (−∞,0)

5. Conclude the boundaries. Since ex never reaches zero, −ex will also never reach zero, meaning the range is all negative real numbers.

Final Answer

Domain: *(−∞,∞), Range: *(−∞,0)

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