Questions: Draw the graph of f(x) = (1/8)^x.

Transcript text: Draw the graph of $f(x)=\left(\frac{1}{8}\right)^{x}$.

Solution

Solution Steps

Step 1: Identify the Function

The function given is $ f(x) = \left(\frac{1}{8}\right)^{x} $.

Step 2: Determine Key Points

To graph the function, we can calculate a few key points:

$ f(-2) = \left(\frac{1}{8}\right)^{-2} = 64 $
$ f(-1) = \left(\frac{1}{8}\right)^{-1} = 8 $
$ f(0) = \left(\frac{1}{8}\right)^{0} = 1 $
$ f(1) = \left(\frac{1}{8}\right)^{1} = \frac{1}{8} \approx 0.125 $
$ f(2) = \left(\frac{1}{8}\right)^{2} = \frac{1}{64} \approx 0.0156 $

Step 3: Describe the Behavior

The function $ f(x) = \left(\frac{1}{8}\right)^{x} $ is an exponential decay function. As $ x $ increases, $ f(x) $ approaches zero. As $ x $ decreases, $ f(x) $ increases rapidly.

Final Answer

The function $ f(x) = \left(\frac{1}{8}\right)^{x} $ is an exponential decay function with key points calculated above.

{"axisType": 3, "coordSystem": {"xmin": -4, "xmax": 4, "ymin": -1, "ymax": 70}, "commands": ["y = (1/8)**x"], "latex_expressions": ["$f(x) = \\left(\\frac{1}{8}\\right)^{x}$"]}

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >