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Mathematics 10C
17. 10C.17. Develop algebraic and graphical reasoning through the study of relations
17.4 Reflection across the y-axis: y = f(-x)
Reflection Across the Y-Axis: y = f(-x)
Discover how replacing x with negative x flips a graph across the y-axis, with clear steps, a point-mapping diagram, and worked examples.
What You'll Learn
Reflecting a function across the y-axis produces a new function g of x equal to f of negative x.
Every point with coordinates x, y on the original graph maps to negative x, y on the reflected graph.
The y-coordinate of each point never changes; only the x-coordinate flips sign.
If a function is even, meaning f of negative x equals f of x, its graph looks identical after this reflection.
Reflecting across the y-axis is different from reflecting across the x-axis, which negates the output instead of the input.
What You'll Practice
1
Reflecting graphs across the y-axis by transforming key points
2
Plotting reflected functions from original coordinate pairs
3
Drawing reflections of cubic and other functions using the mirror image concept
Why This Matters
Understanding reflections across the y-axis is essential for mastering function transformations, which you'll use extensively in precalculus and calculus. This skill helps you visualize symmetry, analyze even and odd functions, and solve real-world problems involving mirror images and symmetrical designs.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Learning resources
Skills
Reflections
Function Transformations
Y-axis Symmetry
Coordinate Manipulation
Graphing Functions
AB Curriculum Aligned