The function has a break at x = 3. We need to evaluate if the function is continuous at x = 3.
As we approach x = 3 from the left hand side we get, g(3 - h) = - (3 - h) / 2 = - 3 / 2
As we approach x = 3 from the right hand side we get, g(3 + h) = - (3+ h) / 2 = - 3 / 2
g(3) = 5
Since the left hand limit = right hand limit, but they ae not equal to the value of the function at the given point, hence the given function is not continuous at x = 3.
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