Graph y=(1/3)^x

Problem

y=(1/3)x

Solution

1. Identify the type of function. This is an exponential decay function because the base b=1/3 is between 0 and 1

2. Determine the y-intercept by substituting x=0 Since (1/3)0=1 the graph passes through (0,1)

3. Calculate additional points to define the shape. For x=1 y=1/3 For x=−1 y=3 For x=2 y=1/9

4. Identify the horizontal asymptote. As x increases toward infinity, y approaches 0 Thus, the horizontal asymptote is y=0

5. Plot the points (−1,3) (0,1) and (1,1/3) and draw a smooth curve that decreases from left to right, staying above the x-axis.

Final Answer

y=(1/3)x

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