 A course on linear functions with the definition, vocabulary and properties as well as the study of percentages is always necessary for your progress. The student will need to have a good grasp of the concept of proportionality which leads to a linear function. Then, he/she must develop the skills to calculate an image or an antecedent, or to draw the curve of a linear function or to determine the value of the directing coefficient in third grade.

## I. Linear functions :

### 1. definition and vocabulary

Definition:

Let “a” be a fixed number. By associating to each number ” x ” a number ” ax ” called ” image of x “, we define a linear function of coefficient a.

This function will be noted as follows: The image of x will be noted: f(x).

x is called the antecedent of f(x)

Example:

Let f be the linear function of coefficient 2.

It is noted : then :

• The image of 5 is: .
• The image of (-3) is: .
• The image of 1 is: .

Remark:

These results can be grouped in a table:

 x 5 -3 1 f(x) 10 -6 2

This is a proportionality table. And the proportionality coefficient that allows to express f(x) as a function of x is 2 ! Hence the equality: .

### 2.graphical representation :

Property and vocabulary:

Let f be the linear function defined by : The set of points with coordinates is called the graphical representation of the linear function.

In a reference frame, this representation is the line passing through :

• The origin of the benchmark.
• The point with coordinates .

We say that this line has the equation: .

“a” is the directing coefficient of the line. It indicates the “inclination” of the right.

### 3.direction of variation of a linear function :

Ownership:
• If a>0 then the linear function is increasing;
• If a<0 then the linear function is decreasing. Remark:

If a = 0, the representation of the line merges with the x-axis.

## II. Linear functions and percentages

### 1. percentages of increase and decrease

Ownership:
• Increasing a number by t% is equivalent to multiplying the number by .
• Decreasing a number by t% is equivalent to multiplying the number by .

Examples:
If a 400 g can is sold with 25% more product, its new mass (in g) is : i.e. m = 500 g.

• In France, a decrease of 4% was recorded on an annual number of 750 000 births.
The new workforce is : i.e. N = 720 000.

### 2. application of percentages to linear functions

 Take 5% of x. Increase x by 5%. Decrease x by 5%. Calculation to be made Multiply by 0.05 Multiply by 1.05 Multiply by 0.95 Linear function   Example: Take 5% of 20 : Increase 20 by 5%: Decrease 20 by 5%: Ownership:

In a general way, we can associate a linear function to any variation of k %.Let us note the function f which to the starting value x associates the value f(x) after variation.

• For an increase of k%, we have .
• For a reduction of k%, we have .
Télécharger puis imprimer cette fiche en PDF

Télécharger ou imprimer cette fiche «linear functions: 3rd grade math course to download in PDF.» au format PDF afin de pouvoir travailler en totale autonomie.

## D'autres fiches dans la section 3rd grade math class

Les dernières fiches mises à jour

Voici la liste des derniers cours et exercices ajoutés au site ou mis à jour et similaire à linear functions: 3rd grade math course to download in PDF. . Mathématiques Web c'est 2 146 115 fiches de cours et d'exercices téléchargées.

Copyright © 2008 - 2023 Mathématiques Web Tous droits réservés | Mentions légales | Signaler une Erreur | Contact

.
Scroll to Top
Mathématiques Web

FREE
VIEW