Graph f(x)=(1/5)^x

Problem

ƒ(x)=(1/5)x

Solution

1. Identify the type of function. This is an exponential function of the form ƒ(x)=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, (1/5)x approaches 0 Therefore, the horizontal asymptote is the line y=0

3. Calculate the y-intercept by evaluating the function at x=0

ƒ(0)=(1/5)0=1

4. Find additional points to plot. Choose x=−1 and x=1 to determine the shape of the curve.

ƒ*(−1)=(1/5)(−1)=5

ƒ(1)=(1/5)1=1/5

5. Sketch the graph by plotting the points (−1,5) (0,1) and (1,0.2) then drawing a smooth curve that decreases from left to right and approaches the x-axis.

Final Answer

The graph of ƒ(x)=(1/5)x is a decreasing exponential curve passing through (0,1) with a horizontal asymptote at y=0

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