Final answer:
The function 1/(x+7) is continuous over the interval (-4,4) because there are no points within this interval where it is undefined or has a discontinuity.
Step-by-step explanation:
The student asked whether the function given by 1/(x+7) is continuous over the interval (-4,4). To determine the continuity of the function over the given interval, we need to analyze the behavior of the function within that interval.
The function 1/(x+7) is undefined at x = -7 because it would result in a division by zero, which is not allowed in mathematics. However, since -7 is not within the interval (-4,4), this does not affect the function's continuity on the interval in question. For all other values of x within the interval (-4,4), the function is defined and behaves normally without any breaks or jumps in the graph.
Therefore, the function is continuous over the interval (-4,4) because it does not have any points within this interval where it is undefined or exhibits a discontinuity.