Function Transformations and Their Effects

This comprehensive page details various effects of function reflections and stretches on graphs, providing a systematic breakdown of common transformations.

The transformations are organized into several categories:

Definition: Vertical shifts $y = f(x) + a$ move the graph up when a is positive and down when a is negative.

Definition: Horizontal shifts $y = f(x + a)$ move the graph left when a is positive and right when a is negative.

Highlight: Reflections can occur in two ways:

• y = -f$x$ reflects the graph across the x-axis
• y = f$-x$ reflects the graph across the y-axis

Example: When dealing with stretches and compressions:

• For y = kf$x$: k > 1 creates a vertical stretch, k < 1 creates a vertical compression
• For y = f(kx): k > 1 creates a horizontal compression, k < 1 creates a horizontal stretch

Vocabulary:

• Stretch: Expansion of the graph along an axis
• Compression: Contraction of the graph along an axis
• Reflection: Mirror image of the graph across an axis

This graph function compression and stretching explained guide serves as a fundamental resource for understanding how mathematical operations transform basic functions into more complex forms.