Understanding Affine Functions and Inequalities

📋 Course Outline

1. Definition and properties of affine functions
2. Determining affine function expression from two points
3. Monotonicity and variation of affine functions based on slope
4. Sign analysis of affine functions and solving inequalities

📖 1. Definition and properties of affine functions

🔑 Key Concepts & Definitions

• Coefficient directeur : a real number that indicates the slope of the straight line representing the affine function.
• Ordonnée à l'origine : a real number that corresponds to the y-intercept of the line, where it crosses the y-axis.
• Fonction affine : a function defined on the interval ] -∞ ; +∞ [ that can be expressed in the form f(x) = mx + p, where m and p are real numbers.
• Une fonction affine : an affine function whose graph is a straight line, possibly passing through the origin.

📝 Essential Points

• An affine function is defined on the entire real line, ] -∞ ; +∞ [, and can be written as f(x) = mx + p.
• The number p is called the ordonnée à l'origine, representing the y-intercept of the graph.
• The number m is called the coefficient directeur, representing the slope of the line.
• The graph of an affine function is a straight line.
• If this line passes through the origin (0,0), the function is called a linear function.

💡 Key Takeaway