Given:-
[tex]y=(\frac{1}{3})^x[/tex]
To graph the image.
So now we find the values of y when the value of x is -3,-2,-1,0,1,2,3.
When x is -3. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^{-3} \\ y=(3)^3 \\ y=27 \end{gathered}[/tex]
So the required value is 27.
when x is -2. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^{-2} \\ y=(3)^2 \\ y=9 \end{gathered}[/tex]
So the required value is 9.
When x is -1. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^{-1} \\ y=(3)^1 \\ y=3 \end{gathered}[/tex]
So the required value is 3.
When x is 0. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^0 \\ y=0 \end{gathered}[/tex]
So the required value is 0.
When x is 1. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^1 \\ y=\frac{1}{3} \end{gathered}[/tex]
So the required value is 1/3.
When x is 2. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^2 \\ y=\frac{1}{9} \end{gathered}[/tex]
So the required value is 1/9.
When x is 3. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^3 \\ y=\frac{1}{27} \end{gathered}[/tex]
So the required value is 1/27.
So the graph looks like,
This is the graph and it decreases from left to right.
