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Write the exponential function.





x

f(x)


-1
8


0
4


1
2


2
1

Write the exponential function.\newline\begin{tabular}{|c|c|}\newline\hlinex x & f(x) f(x) \\\newline\hline1-1 & 88 \\\newline\hline 00 & 44 \\\newline\hline 11 & 22 \\\newline\hline 22 & 11 \\\newline\hline\newline\end{tabular}

Full solution

Q. Write the exponential function.\newline\begin{tabular}{|c|c|}\newline\hlinex x & f(x) f(x) \\\newline\hline1-1 & 88 \\\newline\hline 00 & 44 \\\newline\hline 11 & 22 \\\newline\hline 22 & 11 \\\newline\hline\newline\end{tabular}
  1. Notice pattern: Notice the pattern: each time xx increases by 11, f(x)f(x) is halved. This means the base of the exponential function is 12\frac{1}{2}.
  2. Find initial value: To find the exponential function, we need to find the initial value when x=0x=0. From the table, when x=0x=0, f(x)=4f(x)=4. So the initial value is 44.
  3. Identify exponential function: The exponential function is f(x)=abxf(x) = a \cdot b^x, where aa is the initial value and bb is the base. We have a=4a=4 and b=12b=\frac{1}{2}.
  4. Write function: Write the function: f(x)=4(12)xf(x) = 4 \cdot \left(\frac{1}{2}\right)^x.

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