Graph y=-2^x

Problem

y=−2

Solution

1. Identify the parent function as y=2 which is a basic exponential growth function that passes through (0,1) and (1,2)

2. Apply the transformation by noting the negative sign in front of the base, which represents a reflection across the xaxis.

3. Determine the horizontal asymptote by observing that as x approaches −∞ the value of 2 approaches 0 so y approaches 0 The horizontal asymptote is y=0

4. Calculate key points to plot the curve:

   • If x=−1 y=−2(−1)=−0.5

   • If x=0 y=−2=−1

   • If x=1 y=−2=−2

   • If x=2 y=−2=−4

5. Sketch the graph by plotting these points and drawing a smooth curve that stays below the xaxis, decreasing rapidly as x increases.

Final Answer

y=−2

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