Algebra 1 Chapter 3 Transformations Flashcards

Parent Function

• The parent function for linear equations is expressed as f(x) = x.

Vertical Translations

• f(x) = x + 2: Represents a vertical translation of the graph up 2 units.
• f(x) = x + 12: Indicates a vertical translation up 12 units.
• f(x) = x - 3: Denotes a vertical translation down 3 units.

Horizontal Translations

• f(x) = (x - 4): Signifies a horizontal translation of the graph right 4 units.
• f(x) = (x + 7): Indicates a horizontal translation left 7 units.

Dilation

• f(x) = 5(x): This function shows vertical dilation, resulting in the graph being stretched.
• f(x) = (1/2)x: Represents horizontal dilation, causing the graph to be stretched.
• f(x) = (4x): Indicates horizontal dilation, resulting in the graph being compressed.
• f(x) = (3/5)x: Demonstrates vertical dilation, causing the graph to be compressed.

Translation vs. Dilation

• f(x) = (x - 4): Characterizes the function as a horizontal translation.
• f(x) = (2/19)x: Represents a vertical dilation.

General Concepts

• Translation: A movement of a graph in any direction, including up, down, left, or right.
• Vertical Transition (up): Described by f(x) = x + k (where k > 0) indicating movement k units up.
• Vertical Transition (down): Given by f(x) = x + k (where k < 0) indicating movement |k| units down.
• Horizontal Translation (right): Expressed as f(x) = (x - h) (where h > 0) showing a movement h units right.
• Horizontal Translation (left): Illustrated by f(x) = (x - h) (where h < 0) indicating a movement |h| units left.