Function Transformations and Limits
This page focuses on function transformations and introduces the concept of limits. It begins by explaining how various transformations affect the graph of a function, such as vertical and horizontal shifts, reflections, and stretches.
Highlight: Function transformations include vertical shifts f(x + a), horizontal shifts f(x+a), reflections −f(x and f−x), and stretches (af(x) and f(ax)).
The page then introduces the intuitive notion of limits, discussing two types: direct limits and limits using algebra.
Example: For a direct limit, limx→5 x + 7 = 5 + 7 = 12. For a limit using algebra, limh→0 (3+h² - 9) / h is solved by factoring and simplifying.
These examples demonstrate how to approach different types of limit problems, providing a foundation for more advanced calculus concepts.