Symmetry of Function Graphs Relative to the OX Axis

This page discusses the concept of symetria względem osi OX (symmetry with respect to the OX axis) for function graphs. The main focus is on how to reflect points across the x-axis to create a symmetrical image of the original function.

The page presents a visual representation of this concept, showing how points are reflected across the x-axis. It demonstrates that the x-coordinate remains the same while the y-coordinate changes sign.

Example: Point A(-4, 2) is reflected to A'(-4, -2), illustrating that the x-coordinate (-4) stays the same, but the y-coordinate changes from 2 to -2.

Several other examples are provided to reinforce this concept:

• B(-3, 4) is reflected to B'(-3, -4)
• C(-1, 2) is reflected to C'(-1, -2)
• A(2, 3) is reflected to A'(2, -3)

The page also includes a mathematical representation of this symmetry:

Definition: For a function f(x), its reflection across the OX axis is given by -f(x).

An example of this is provided using the function f(x) = 2x - 3. Its reflection is -f(x) = -$2x - 3$ = -2x + 3.

Highlight: To create a symmetrical image of a function graph with respect to the OX axis, select characteristic points and reflect them across the x-axis by changing the sign of their y-coordinates.

The page concludes with additional examples of point reflections:

• E(3, 3) is reflected to E'(3, -3)
• D(2, 2) is reflected to D'(2, -2)
• F(4, 2) is reflected to F'(4, -2)

This comprehensive explanation and visual representation help students understand the concept of symetria względem osi OX and how to apply it to function graphs.