Exercise 3-4: Function Analysis and Continuity

This section examines students' comprehension of function behavior, continuity, and asymptotes. The problems involve analyzing piecewise functions and their properties.

Vocabulary: Asymptotes are lines that a function approaches but never touches as x approaches infinity.

Definition: A function is continuous at a point if the limit at that point exists and equals the function value.

Example: The analysis of continuity at x=-1 involves checking both left and right-hand limits.

Function Analysis and Continuity

This section covers function analysis, including continuity studies and asymptote determination. The problems focus on complex rational functions and their behavior.

Definition: Continuity analysis involves examining function behavior at critical points and determining various types of asymptotes.

Example: The function analysis includes studying continuidad y asíntotas de una función with specific attention to vertical, horizontal, and oblique asymptotes.