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 $f\,:\,x\,\mapsto \,0,05\,x$ $g\,:\,x\,\mapsto \,1,05\,x$ $h\,:\,x\,\mapsto \,0,95\,x$ Example: Take 5% of 20 : $f(20)\,=\,0,05\,\times \,20\,=\,1$ Increase 20 by 5%: $g(20)\,=\,1,05\,\times \,20\,=\,21$ Decrease 20 by 5%: $h(20)\,=\,0,95\,\times \,20\,=\,19$
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 .

Cette publication est également disponible en : Français (French) العربية (Arabic)

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

Télécharger nos applications gratuites Mathématiques Web avec tous les cours,exercices corrigés.

• 95
The pyramid and the cone are a very important chapter in eighth grade math. The student will need to know all the definitions as well as the different vocabulary regarding faces, vertex, base and height. Thus, it must also develop skills in calculations with the formulas of volume: I. The…
• 95
The course on the formulas of the volume of a solid and the study of sections of solids in space with situations of reduction or enlargement in third grade (3ème) is essential for the progression of the student. The student will need to know the formulas by heart and know…
• 95
The course on equations of the first degree with one unknown with the definition and the properties of solving an equation and then the method of solving problems in the fourth grade (4e) is to be understood completely. The student should be able to solve an equation with the various…
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