To solve the question, choose values for x to find its corresponding image y. Then, plot the points and connect them.
Step 01: Choosing x = -2.
Substituting x by -2 in the equation:
[tex]\begin{gathered} y=2\cdot3^{-2} \\ y=2\cdot(\frac{1}{3})^2 \\ y=2\cdot\frac{1}{9} \\ y=\frac{2}{9} \end{gathered}[/tex]
So, the first point is (-2, 2/9).
Step 02: Choosing x = -1.
Substituting x by -1 in the equation:
[tex]\begin{gathered} y=2\cdot3^{-1} \\ y=2\cdot(\frac{1}{3})^1 \\ y=2\cdot\frac{1}{3} \\ y=\frac{2}{3} \end{gathered}[/tex]
So, the second point is (-1, 2/3).
Step 03: Choosing x = 0.
Substituting x by 0 in the equation:
[tex]\begin{gathered} y=2\cdot3^0 \\ y=2\cdot1 \\ y=2 \end{gathered}[/tex]
So, the third point is (0, 2).
Step 04: Choosing x = 1.
Substituting x by 1 in the equation:
[tex]\begin{gathered} y=2\cdot3^1 \\ y=2\cdot3 \\ y=6 \end{gathered}[/tex]
So, the fourth point is (1, 6).
Step 05: Write the points in a table.
x y (x, y)
-2 2/9 (-2, 2/9)
-1 2/3 (-1, 2/3)
0 2 (0, 2)
1 6 (1, 6)
Step 06: Plot the points and connect them.
The figure below shows the points and the graph.
Done! Your question is solved!
