T Misconceptions Transformations of Functions

The video addresses common misconceptions about function transformations, providing false statements and counterexamples. It covers how horizontal shifts and reflections affect domain, the impact of vertical shifts and reflections on range, and the misconception that horizontal stretches alter vertical asymptotes. The importance of applying transformations in the correct order is also discussed, emphasizing the need to follow the order of operations.

What is a common misconception regarding the effect of horizontal shifts on the domain of a function?

Explain how reflections about the Y-axis can impact the domain of a function.

Discuss why the statement 'all functions with a vertical shift and reflection about the X-axis must have a change in the range' is not universally true.

What happens to vertical asymptotes when a horizontal stretch is applied to a function?

How do vertical and horizontal asymptotes behave under transformations such as stretching or compressing?

Describe the importance of the order of operations when applying transformations to a graph.

What are some examples of false statements related to transformations of functions that could challenge students?