Overview

Financial and Workplace Mathematics 120

Geometry

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

4.9 Reflection across the x-axis: y = -f(x)

Reflection Across the x-axis: y = -f(x)

See exactly how the rule y = -f(x) flips a graph over the x-axis, with clear steps and worked examples for parabolas and absolute value graphs.

What You'll Learn

Reflecting a graph across the x-axis multiplies every output value by negative one, giving the new equation y = -f(x).

Every point (x, y) on the original graph moves to (x, -y) on the reflected graph, so the x-coordinates never change.

Maximum points become minimum points and minimum points become maximum points, while x-intercepts stay exactly where they were.

The domain of the reflected function is the same as the original, but the range flips sign.

A common mistake is negating the input instead of the output; -f(x) is not the same as f(-x), which reflects across the y-axis instead.

What You'll Practice

Reflecting graphs across the x-axis by transforming coordinate points

Converting positive y-values to negative y-values and vice versa

Plotting reflected points and sketching transformed functions

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:

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

This Unit Includes

2 Video lessons

Learning resources

Skills

Reflections

Function Transformations

Coordinate Geometry

Graphing

Invariant Points

Negative Functions

NB Curriculum Aligned