Chapter 23.1
Transformations of functions: Horizontal translations
What You'll Learn
Identify horizontal translations by recognizing changes to x-values in function notation
Apply the rule that f(x - h) shifts a graph h units right while f(x + h) shifts h units left
Determine how subtracting or adding inside a function affects graph position horizontally
Use key points like vertices and intercepts to accurately sketch translated graphs
Verify horizontal shifts by tracking coordinate changes while keeping y-values constant
What You'll Practice
1
Shifting quadratic functions left and right by modifying x-values
2
Sketching translated graphs using the three-point method with intercepts
3
Comparing original and translated functions to identify direction and distance of shift
4
Working with expressions like f(x - a) and f(x + a) to transform graphs
Why This Matters
Horizontal translations are essential for understanding how functions transform across coordinate planes. You'll use this skill constantly in algebra, trigonometry, and calculus when working with shifted parabolas, sine waves, and other function families. Mastering this concept helps you quickly visualize and graph complex functions.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Skills
Horizontal Translation
Function Transformations
Graph Shifting
Coordinate Plane
Quadratic Functions
Function Notation
