Which of the following functions are continuous for all values in their domain? Justify your answers.


a. a(t)=altitude of a skydiver t seconds after jumping from a plane

Verified step by step guidance

1. Step 1: Understand the concept of continuity. A function is continuous at a point if the limit of the function as it approaches the point from both sides is equal to the function's value at that point. A function is continuous over an interval if it is continuous at every point in that interval.
2. Step 2: Consider the function a(t) = altitude of a skydiver t seconds after jumping from a plane. This function represents the altitude of a skydiver as a function of time.
3. Step 3: Analyze the behavior of the function a(t). Initially, the skydiver is at a certain altitude, and as time progresses, the altitude decreases as the skydiver falls.
4. Step 4: Determine if there are any points of discontinuity. In the context of a skydiver's altitude, there are no sudden jumps or breaks in the altitude as time progresses, assuming no external forces like parachute deployment are considered.
5. Step 5: Conclude that the function a(t) is continuous for all values in its domain, as the altitude changes smoothly over time without any abrupt changes.