Answer:
The correct answer is the third graph.
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
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.