Graph f(x)=(1/4)^x

Problem

ƒ(x)=(1/4)x

Solution

1. Identify the type of function. This is an exponential function of the form ƒ(x)=bx where the base b=1/4 Since 0<b<1 the graph represents exponential decay.

2. Determine the horizontal asymptote. As x increases toward infinity, (1/4)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)=(1/4)0=1

4. Find additional points to determine the shape of the curve.

ƒ*(−1)=(1/4)(−1)=4

ƒ(1)=(1/4)1=1/4

ƒ(2)=(1/4)2=1/16

5. Plot the points (−1,4) (0,1) and (1,0.25) and draw a smooth curve that approaches the x-axis as x moves to the right.

Final Answer

ƒ(x)=(1/4)x

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