Discuss the continuity of the function .
First, note that the domain of the function is .
Due to the presence of the absolute value, the function will be
defined differently depending on whether is greater than or less
than 7. Therefore, the function can be expressed as
The function is continuous over each subinterval of its domain, as each part of its rule is a polynomial.
Now consider continuity of the function at each point where the rule differs: at and .
Therefore, the function is continuous at as .
Therefore, the function is discontinuous at as .
Hence the function is continuous on .