See graph below
Explanation:[tex]f(x)\text{ = }-\frac{1}{2}\cos (\frac{-2}{3}x)[/tex]
From the equation, the highest point of the graph = -0.5
y = -0.5
To p;ot the graph, we can ssign values for x, inorder to get corresponding y values
let x = -3π/2, 0, 3π/2
[tex]\begin{gathered} \text{when x = -}\frac{3\pi}{2} \\ f(x)\text{ = }-\frac{1}{2}\cos (\frac{-2}{3}\times\text{-}\frac{3\pi}{2})\text{ } \\ f(x)\text{ = }-\frac{1}{2}\cos (-1\times\text{-}\pi)\text{ = }-\frac{1}{2}\cos (\pi) \\ 1\pi\text{ = 180 degr}es,\text{ }\cos (\pi)\text{ = cos 180}\degree \\ f(x)\text{ = -0.5(-1) = 0.5} \\ \\ \text{when x = 0} \\ f(x)\text{ = }-\frac{1}{2}\cos (\frac{-2}{3}\times\text{0})\text{ } \\ f(x)\text{ = }-\frac{1}{2}\cos (0)\text{ = -0.5(1)} \\ f(x)\text{ }=\text{ -0.5} \end{gathered}[/tex][tex]\begin{gathered} \text{when x = }\frac{3\pi}{2} \\ f(x)\text{ = }-\frac{1}{2}\cos (\frac{-2}{3}\times\frac{3\pi}{2})\text{ } \\ f(x)\text{ = }-\frac{1}{2}\cos (-1\times\pi)\text{ = }-\frac{1}{2}\cos (-\pi) \\ 1\pi\text{ = 180 degr}es,\text{ }\cos (-\pi)\text{ = cos -180}\degree \\ f(x)\text{ = -0.5( cos (-180}\degree)) \\ f(x)\text{ = 0.5} \end{gathered}[/tex]
Plotting the graph:
This graph doesn't have the same readings in its x axis as the graph you attached. It is meant as a guide on how the curve should look like
plotting the points on the given graph (sketch):
