Understanding Affine Functions and Inequalities

From the study guide

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

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Practice quiz preview

1. How does an affine function differ from a linear function in terms of their graphs and algebraic expressions?

2. How do the methods for determining the coefficient directeur and the constant term differ when finding the affine function expression from two points?

3. What is an affine function?

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Flashcard preview

Affine functions — definition?

Functions of the form f(x) = mx + p, with straight-line graphs.

From two points — find affine formula?

Calculate slope m, then find p by substitution.

Affine function — definition?

f(x) = mx + p, line graph.

p — role?

Y-intercept of the line.

m — role?

Slope of the line.

From two points — m formula?

m = (yB - yA) / (xB - xA).

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Frequently asked questions

What does the Understanding Affine Functions and Inequalities study guide cover?

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How many questions are in the Understanding Affine Functions and Inequalities quiz?

The practice quiz has 5 multiple-choice questions, each with an explanation. Use it to check what you know and find your gaps.

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