Graph y=(1/6)^x

Problem

y=(1/6)x

Solution

1. Identify the function type as an exponential decay function because the base b=1/6 is between 0 and 1

2. Determine the y-intercept by substituting x=0 into the equation, which gives y=(1/6)0=1

3. Calculate additional points to define the shape: when x=−1 y=(1/6)(−1)=6 when x=1 y=(1/6)1=1/6

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

5. Sketch the curve passing through the points (−1,6) (0,1) and (1,1/6) showing the graph decreasing from left to right.

Final Answer

y=(1/6)x

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