Find the Domain and Range -e^x

Problem

ƒ(x)=−e^x

Solution

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

2. Determine the domain. Exponential functions of the form e^x 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 e^x is always strictly greater than zero for all real x

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

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

Final Answer

Domain: *(−∞,∞), Range: *(−∞,0)

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