Find the Domain and Range f(x)=e^x-1

Problem

ƒ(x)=ex−1

Solution

1. Identify the domain of the natural exponential function ex which is defined for all real numbers.

2. Determine the domain of ƒ(x) by noting that subtracting a constant does not restrict the input values.

3. State the domain in interval notation.

D=(−∞,∞)

4. Identify the range of the parent function ex which is (0,∞)

5. Apply the vertical shift to find the range of ƒ(x) by subtracting 1 from the lower bound of the parent range.

6. State the range in interval notation, noting that the function approaches but never reaches the horizontal asymptote y=−1

R=(−1,∞)

Final Answer

Domain: *(−∞,∞), Range: *(−1,∞)

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