Overview

Financial and Workplace Mathematics 120

Geometry

4. Demonstrate an understanding of transformations of a 2-D shape or a 3-D object

4.8 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

Reflecting graphs across the y-axis by transforming key points

Plotting reflected functions from original coordinate pairs

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:

Transformations of functions: Horizontal translations Transformations of functions: Vertical translations

This Unit Includes

2 Video lessons

Learning resources

Skills

Reflections

Function Transformations

Y-axis Symmetry

Coordinate Manipulation

Graphing Functions

NB Curriculum Aligned