The equation is
[tex]y=\frac{3^x}{4}[/tex]
Set x=-2, we get
[tex]y=\frac{3^{-2}}{4}[/tex][tex]\text{ Use }a^{-n}=\frac{1}{a^n}\text{.}[/tex]
[tex]y=\frac{1}{3^2\times4}=\frac{1}{9\times4}[/tex]
[tex]y=\frac{1}{36}=0.028[/tex][tex]\text{The point is (-2,0.028})[/tex]
set x=-1, we get
[tex]y=\frac{3^{-1}}{4}[/tex]
[tex]y=\frac{1}{3\times4}=\frac{1}{12}=0.08[/tex][tex]\text{The point is (-1,0.08})[/tex]
Set x=0, we get
[tex]y=\frac{3^0}{4}=\frac{1}{4}=0.25[/tex]
[tex]\text{The point is (0,0.25})[/tex]
Set x=1,we get
[tex]y=\frac{3^1}{4}=\frac{3}{4}[/tex]
[tex]\text{The point is (1,}\frac{3}{4})[/tex]
Set x=2, we get
[tex]y=\frac{3^2}{4}=\frac{9}{4}[/tex]
[tex]\text{The point is (2,}\frac{9}{4})[/tex]
The table is
[tex]\begin{gathered} x\text{ = -2 -1 0 1 2 4} \\ y\text{ = }\frac{1}{36}\text{ }\frac{1}{12}\text{ }\frac{1}{4}\text{ }\frac{3}{4}\text{ }\frac{9}{4}\text{ }\frac{81}{4} \end{gathered}[/tex]
[tex]\begin{gathered} x\text{ = -2 \_\_\_\_\_\_-1 \_\_\_\_\_\_0\_\_\_ \_\_\_1\_\_\_\_\_\_\_ 2 } \\ y\text{ = 0.028\_\_\_\_0.083\_\_\_\_}0.25_{---}_{}0.75--2.25 \end{gathered}[/tex]
Mark all the points on the graph and connect them all as follows.
