Graph f(x)=e^x

Problem

ƒ(x)=ex

Solution

1. Identify the function as a basic exponential function where the base is Euler's number e≈2.718

2. Determine the domain and range. The domain is all real numbers (−∞,∞) and the range is all positive real numbers (0,∞)

3. Find the y-intercept by evaluating ƒ(0) Since e0=1 the graph passes through (0,1)

4. Identify the horizontal asymptote. As x approaches negative infinity, ex approaches 0 so the line y=0 is a horizontal asymptote.

5. Plot additional points to determine the shape. For x=1 ƒ(1)=e≈2.718 For x=−1 ƒ*(−1)=1/e≈0.368

6. Sketch a smooth curve that increases rapidly for x>0 and flattens toward the x-axis for x<0

Final Answer

ƒ(x)=ex

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