Graph f(x)=(1/3)^x

Problem

ƒ(x)=(1/3)x

Solution

1. Identify the type of function, which is an exponential function of the form ƒ(x)=bx where the base b=1/3

2. Determine the behavior of the graph. Since 0<1/3<1 the function represents exponential decay, meaning the graph will decrease from left to right.

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

ƒ(0)=(1/3)0=1

4. Calculate additional points to define the shape of the curve.

ƒ*(−1)=(1/3)(−1)=3

ƒ(1)=(1/3)1=1/3

ƒ(2)=(1/3)2=1/9

5. Identify the horizontal asymptote. As x increases toward infinity, ƒ(x) approaches 0

Horizontal Asymptote: *y=0

6. Plot the points (−1,3) (0,1) and (1,1/3) and draw a smooth curve that approaches the x-axis but never touches it.

Final Answer

ƒ(x)=(1/3)x

Want more problems? Check here!