1.2 Combining Functions; Shifting and Scaling Graphs

Introduction to Function Operations00:00:00

Overview of combining functions using addition, subtraction, multiplication, and division, emphasizing that the domain of these combined functions is the intersection of the original domains.

Arithmetic Combinations and Domains00:02:46

Deep dive into how arithmetic operations interact with domains, noting that division specifically requires excluding x-values that result in a zero denominator.

Function Composition00:07:35

Explaining composite functions as a chain where one output becomes another input, including how to determine the domain by checking valid inputs for both inner and outer functions.

Vertical and Horizontal Shifting00:11:43

Techniques for shifting graphs vertically (adding to the output) and horizontally (adding to the input), noting that horizontal shifts behave in the opposite direction of the constant.

Scaling and Reflecting Graphs00:14:40

How multiplying by constants impacts the shape of a graph, covering vertical stretching/compression and horizontal scaling, as well as reflections across the x and y axes.

Combining Multiple Transformations00:20:56

Applying multiple transformations, such as scaling and reflection, into a single algebraic step by modifying the input or the entire function output.

Conclusion and Review00:25:35

Summary of the main concepts and final practice problems designed to test understanding of function composition and sequential graph transformations.