This page focuses on practicing basic transformations through visual representations and mathematical notation.

Vocabulary: Translations/Shifts refer to movement of the function graph in any direction without changing its shape.

Example: Detailed exploration of transformations:

• f(x) = f$x-1$ represents a right shift
• f(x) = f(x)-2 represents a downward shift

Highlight: The page emphasizes the distinction between horizontal and vertical transformations through graphical representations.

This page advances to more complex transformations combining multiple operations.

Example: Analysis of complex functions:

• f(x) = 2f$x+3$ combines stretching and left shift
• f(x) = -f(x) demonstrates reflection
• f(x) = -2f(x)+1 combines reflection, stretching, and vertical shift

Highlight: Each transformation is broken down into its component parts for clearer understanding.

This page explores how to analyze and describe multiple transformations in sequence.

Definition: Multiple transformations must be applied in a specific order for correct results.

Example: The transformation y = -2f$x+3$ is broken down into:

1. Reflection over X-axis
2. Vertical stretch by factor of 2
3. Horizontal shift left 3 units

This page focuses on constructing function notation from described transformations.

Highlight: Students learn to convert verbal descriptions of transformations into proper function notation.

Example: Converting "reflection over x-axis, horizontal shift 1 unit left, vertical shift 2 units down" into f(x)= -f$x+1$-2

This page provides practical applications and graphing exercises.

Example: Students practice graphing transformations and determining specific function values:

• g(x) = f$x-3$+1
• h(x) = g$x+2$-3
• g(x) = f$x-2$-1

Highlight: The exercises emphasize both graphical interpretation and numerical computation of transformed functions.

This page introduces the fundamental concepts of transformations in functions, focusing on the absolute value parent function.

Definition: A transformation changes the position or size of a figure and can be applied to parent functions.

Example: Using the absolute value function f(x) = |x| as the parent function, various transformations are explored:

• f(x) = |x| + 2 (shift up 2)
• f(x) = |x| - 2 (shift down 2)
• f(x) = 2|x| (stretch by 2)
• f(x) = -|x| (reflection)

Highlight: The standard notation f(x) = af$x-h$+k represents all transformations where:

• 'a' controls stretching/shrinking and reflection
• 'h' determines horizontal shift
• 'k' determines vertical shift