Page 1: Understanding Parent Functions and Their Properties

This page introduces various fundamental parent functions and their characteristics, with particular emphasis on تطبيقات القيمة المطلقة في الوظائف. The content explores different types of mathematical functions including absolute value, quadratic, square root, linear, and inverse functions.

Definition: Parent functions are the simplest form of a function family, serving as the basis for more complex variations.

Example: In a linear function where input increases by 2, the output increases by 3, demonstrating a consistent rate of change.

Vocabulary: Domain refers to all possible input values, while range encompasses all possible output values.

Highlight: The relationship between linear and inverse functions demonstrates العلاقة بين الدوال الخطية و العكسية, where y=x becomes y=1/x in the inverse form.

Definition: Absolute value function |x| represents the distance of a number from zero on a number line.

The page details various function types:

• Absolute value function $y = |x|$
• Quadratic function $y = x²$
• Square root function $y = √x$
• Linear function $y = x$
• Inverse function $y = 1/x$
• Cubic function $y = x³$
• Exponential function $y = 2ˣ$

Each function type is characterized by its unique behavior with input and output values. For instance, the quadratic function shows a parabolic shape, while the absolute value function creates a V-shaped graph. The exponential function demonstrates rapid growth, and the cubic function combines elements of both positive and negative growth depending on the input values.