Graph y=(1/5)^x

Problem

y=(1/5)x

Solution

1. Identify the type of function. This is an exponential function of the form y=bx where the base b=1/5 Since 0<b<1 the graph represents exponential decay.

2. Determine the horizontal asymptote. As x increases toward infinity, y approaches 0 Therefore, the horizontal asymptote is the line y=0

3. Calculate the y-intercept by setting x=0

y=(1/5)0=1

The y-intercept is (0,1)

4. Find additional points to determine the shape of the curve.
   If x=−1

y=(1/5)(−1)=5

If x=1

y=(1/5)1=1/5=0.2

5. Sketch the curve. Plot the points (−1,5) (0,1) and (1,0.2) Draw a smooth curve that decreases from left to right, passing through these points and approaching the x-axis (y=0 as x becomes large.

Final Answer

y=(1/5)x

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