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Overview
Pre-Calculus 12
Relations and Functions
19. Graph and analyze radical functions
19.1 Radical functions and transformations
Transformations of Radical Functions
Shift, stretch, or reflect a square root function using the same rules as any other function.
What You'll Learn
h shifts the graph horizontally; k shifts it vertically.
a controls vertical stretch/reflection; b controls horizontal stretch/reflection.
y = square root of (x-2) plus 1 shifts the base curve right 2, up 1.
The starting point moves from (0,0) to (2,1) under that shift.
The domain shifts with the graph -- always re-solve inside the radical is at least 0.
What You'll Practice
1
Graphing radical functions using tables of values and coordinate mapping
2
Applying horizontal and vertical transformations to square root functions
3
Finding domain and range from equations without graphing
4
Mapping points from basic to transformed radical functions
Why This Matters
Mastering radical function transformations builds your ability to visualize and analyze function behavior quickly. These skills are essential for precalculus, calculus, and modeling real-world phenomena like pendulum motion and electrical circuits where square root relationships appear.
This Unit Includes
5 Video lessons
Learning resources
Skills
Radical Functions
Transformations
Domain and Range
Coordinate Mapping
Square Roots
Function Graphing
Horizontal Translation
Vertical Reflection
NS Curriculum Aligned