Graph y=-e^x

Problem

y=−ex

Solution

1. Identify the parent function, which is y=ex This is a basic exponential growth function that passes through (0,1) and has a horizontal asymptote at y=0

2. Apply the transformation for the negative sign in front of the function. The negative sign in y=−ex represents a reflection across the xaxis.

3. Determine key points by substituting values for x If x=0 then y=−e0=−1 If x=1 then y=−e1≈−2.718

4. Identify the asymptote of the transformed function. Since the reflection is vertical, the horizontal asymptote remains at y=0

5. Sketch the graph by plotting the points (0,−1) and (1,−e) and drawing a curve that approaches y=0 as x→−∞ and decreases rapidly as x→∞

Final Answer

y=−ex

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