The endpoint and other points are plotted in the graph attached.
What is a ray?
A ray is a line that starts from a fixed point but never ends. The start point is called the endpoint of the ray.
How do we solve the given question?
To solve the given question with piecewise functions,
g(x)={−2x, x≥3
{ −(1/3)x−5, x≤3
we first define its endpoint. The endpoint of a piecewise function is the point where the pieces give the same value. Since both the pieces are defined for x=3, we can say that that is the endpoint of the ray.
Calculating g(3),
g(3) = -2(3) or g(3) = -(1/3)(3) - 5
or, g(3) = -6 or g(3) = -1 - 5 = -6
So, both the pieces give g(3) = -6. We plot this as our endpoint (plotted in the black color dot in the graph).
Now we define one point on every piece,
For g(x) = -2x, x ≥3, we take x = 4
g(4) = -2*4 = -8
For g(x) = -(1/3)x - 5, x≤3, we take x = 0
g(0) = -(1/3)*0 - 5 = -5
(These two points are plotted as red dots in the graph)
The graph is attached for the solution.
Learn more about piecewise functions at
https://brainly.com/question/18499561
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