Graph y=(1/2)^x

Problem

y=(1/2)x

Solution

1. Identify the type of function, which is an exponential decay function because the base b=1/2 is between 0 and 1

2. Determine the y-intercept by substituting x=0 into the equation, giving y=(1/2)0=1

3. Calculate additional points to define the shape of the curve, such as (−1,2) (−2,4) (1,0.5) and (2,0.25)

4. Identify the horizontal asymptote, which is the line y=0 (the x-axis), as the value of y approaches 0 but never reaches it as x increases.

5. Sketch the graph by plotting the points and drawing a smooth curve that decreases from left to right, passing through (0,1) and approaching the x-axis.

Final Answer

y=(1/2)x

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