Answer:
The correct answer is the third graph.
Step-by-step explanation:
The given function is a piecewise funciton which can be defined as a function determined by sub-functions. The result of these functions is a complex behaviour.
In this case, the given function is represents by two linear functions, the first one crosses the origin and has a decreasing behaviour, we know this because its equation is
[tex]y=-x[/tex]
All linear function with no constant term must pass through the origin. Also, this function is defined to every value greater than -3, which means after x=-3, the function is decreasing and passes through the origin.
The second sub-function is a increasing linear function which has y-intercept at 6.
So, the correct answer is the third graph.
Why?
Because the second graph is not a function, it's just a relation. If you apply the vertical line test, it will intercept to points of the figure, which indicates it's not a function.
Now, the first graph is a function but doesn't have the sub-functions that the piecewise function indicates.
