Page 2: Reflections and Symmetry

This page focuses on two additional important przekształcenia wykresów funkcji (function graph transformations): reflections across the x-axis and y-axis.

Definition:

5. -f(x): Reflection across the x-axis (Ox)
6. f(-x): Reflection across the y-axis (Oy)

The page provides visual representations of these reflections, showing how they affect the original function f(x).

Highlight: Reflection across the x-axis (-f(x)) creates a mirror image of the function with respect to the x-axis, effectively flipping it vertically.

Vocabulary: Symetria względem osi OX i OY refers to symmetry with respect to the x-axis and y-axis.

The page emphasizes the importance of understanding these reflections in the context of function transformations. It shows how the graph of g(x) = -f(x) relates to the original function f(x), and similarly for g(x) = f(-x).

Example: For a function f(x) = |x| (absolute value function), its reflection across the y-axis would be f(-x) = |-x|, which is identical to the original function due to the properties of absolute value.

These reflections are crucial in understanding the behavior of various functions and their transformations, particularly when dealing with even and odd functions or analyzing symmetry in mathematical models.