The French method of drawing curves is very systematic:

*“Pratique de l’etude d’une fonction” *

Let * f* be the function represented by the curve

**C**Steps:

1. Simplify ** f(x)**. Determine the

**Domain of definition**(

**D**) of

**;**

*f*2. Determine the

**sub-domain E**of D, taking into account of the

**periodicity**(eg. cos, sin, etc) and

**symmetry**of

*;*

**f**3. Study the

**Continuity**of

**;**

*f*4. Study the

**derivative**of

*and determine*

**f****f'(x)**;

5. Find the

**limits**of

*within the boundary of the intervals in E;*

**f**6. Construct the Table of Variation;

7. Study the

**infinite**branches;

8. Study the remarkable points: point of

**inflection**,

**intersection**points with the X and Y axes;

9. Draw the representative curve

**C**.

Example:

$latex displaystyletext{f: } x mapsto frac{2x^{3}+27}{2x^2}$**Step 1**: Determine the Domain of Definition D

D = R* = R –…

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