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Algebra 2
15. Families of Functions
15.4 Reflection across the x-axis: y = -f(x)
Reflection across the x-axis: y = -f(x)
What You'll Learn
Recognize that y = -f(x) creates a reflection across the x-axis
Understand that the negative sign outside f(x) belongs to y, not x
Apply the rule that all y-coordinates divide by -1 during x-axis reflection
Identify invariant points that remain unchanged after reflection
Distinguish between x-axis reflections (y = -f(x)) and y-axis reflections (y = f(-x))
What You'll Practice
1
Reflecting graphs across the x-axis by transforming coordinate points
2
Converting positive y-values to negative y-values and vice versa
3
Plotting reflected points and sketching transformed functions
4
Verifying reflections by comparing original and reflected coordinates
Why This Matters
Mastering x-axis reflections is essential for understanding function transformations throughout algebra and precalculus. You'll use this skill to graph absolute value functions, analyze trigonometric functions, and solve real-world problems involving symmetry and inverse relationships.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Learning resources
Skills
Reflections
Function Transformations
Coordinate Geometry
Graphing
Invariant Points
Negative Functions
