Answer
Logarithmic function
Work Step by Step
First calculate slope of two consecutive ordered pair coordinates:
The coordinates are \[\left( \tfrac{1}{3},-1 \right),\left( 1,0 \right),\left( 3,1 \right),\left( 9,2 \right),\text{ and}\left( 27,3 \right)\].
\[\text{Since, }m=\left( \frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)\],
Now, calculate slopes of two consecutive ordered pair of coordinates:
\[\begin{align}
& {{m}_{1}}=\left( \frac{0+1}{1-\frac{1}{3}} \right)=\frac{3}{2}=1.5 \\
& {{m}_{2}}=\left( \frac{1-0}{3-1} \right)=\frac{1}{2}=0.5 \\
& {{m}_{3}}=\left( \frac{2-1}{9-3} \right)=\frac{1}{6}=0.1666 \\
& {{m}_{4}}=\left( \frac{3-2}{27-9} \right)=\frac{1}{18}=0.055
\end{align}\]
It can be seen that slopes of any two consecutive coordinate pairs are positive, and slope is decreasing as x increasing. It is the property of logarithmic function.
Therefore, the ordered pair value of this table represents the graph of a logarithmic function.
