Graph f(x)=2^(-x)

Problem

ƒ(x)=2(−x)

Solution

1. Identify the function type as an exponential decay function, which can be rewritten using the property of negative exponents.

ƒ(x)=(1/2)x

2. Determine the y-intercept by evaluating the function at x=0

ƒ(0)=2=1

3. Calculate several points to define the shape of the curve.

ƒ*(−2)=2(−(−2))=4

ƒ*(−1)=2(−(−1))=2

ƒ(1)=2(−1)=0.5

ƒ(2)=2(−2)=0.25

4. Identify the horizontal asymptote. As x increases toward infinity, 2(−x) approaches 0

Asymptote: *y=0

5. Plot the points (−2,4) (−1,2) (0,1) (1,0.5) and (2,0.25) on a coordinate plane and draw a smooth curve that approaches the x-axis but never touches it.

Final Answer

ƒ(x)=2(−x)

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