Reflections (Edexcel A-Level Mathematics): Flashcards

$y = -f(x)$ flips the graph across the $x$-axis.

It maps $(x, y)$ to $(x, -y)$ on the transformed graph.

All positive $y$-values become negative and vice versa.

$y = f(-x)$ reflects the graph across the $y$-axis.

It maps $(x, y)$ to $(-x, y)$ on the transformed graph.

$y = -f(-x)$ rotates the graph 180 degrees around the origin.

The reflection is not defined since $\sqrt{x}$ is for $x \geq 0$.

$y = -x^2 + 4x - 3$ after reflecting across the $x$-axis.

It returns to the original function $1/x$ after reflections.

They help predict and analyze functions’ behavior.