Learn about horizontal and vertical expansions and compressions (aka 'stretches') and how they occur in the graphs of functions when x is replaced with bx or y with ay in the equations of functions. Concepts are addressed three ways: graphically, numerically, and algebraically, ie. with graphs, points and tables, and equations.
See the rest of my videos covering other Function Transformations concepts:    • ★ Function Transformations [Chapter 1...  

Corresponds to chapter 1, section 1.2 in McGraw-Hill's Pre-Calculus 12, but also fits with the Function Transformations unit from almost any other Pre-Calculus course or textbook.

My instructional approach emphasizes conceptual understanding of and connections between concepts and ideas, rather than just pure memorization.

A PDF copy of the 'Video Guide' document used in these videos as well as lots of other resources are available at https://drive.google.com/drive/folder...

#precalc12bytheaamg

00:00 Introduction
00:22 Expansions & Compressions of a Function Visually
02:09 Example 1a: Examine Vertical Stretches Numerically
05:55 Example 1b: Examine Vertical Stretches Graphically
08:41 Example 2a: Examine Horizontal Stretches Numerically
12:19 Example 1b: Examine Horizontal Stretches Graphically
16:17 Example 3: Determining the Equation of Expanded/Compressed Graphs
21:04 Example 4: Graphing Expanded/Compressed Functions
27:11 Example 5: Write the Equation of Expanded/Compressed Functions
30:04 SUMMARY of Horizontal & Vertical Expansions/Compressions (Stretches)
33:43 Wrap Up and End Screen