أسيمبتوتات وفروع الدالة

<p>إذا كانت $ ext{lim}_{x o ext{∞}} [f(x) - ax] = ext{∞}$ و $a eq 0$. (C)</p> Signup and view all the answers

<p>$y = a$ حيث تمثل $a$ قيمة ثابتة. (D)</p> Signup and view all the answers

<p>تفتح في اتجاه اليسار. (A)</p> Signup and view all the answers

<p>فتح القطع الناقص بشكل أفقي. (C)</p> Signup and view all the answers

<p>إذا كانت $ ext{lim}_{x o ext{∞}} [f(x) - 0] = 0$. (C)</p> Signup and view all the answers

<p>La fonction a une asymptote horizontale si $ ext{lim}<em>{x o ext{∞}} f(x) = a$ et $ ext{lim}</em>{x o - ext{∞}} f(x) = a$.</p> Signup and view all the answers

<p>Une asymptote verticale existe si $ ext{lim}<em>{x o a} f(x) = ext{∞}$ ou $ ext{lim}</em>{x o a} f(x) = - ext{∞}$.</p> Signup and view all the answers

<p>Une asymptote oblique est présente si $ ext{lim}<em>{x o ext{∞}} [f(x) - (ax + b)] = 0$ et $ ext{lim}</em>{x o - ext{∞}} [f(x) - (ax + b)] = 0$.</p> Signup and view all the answers

<p>Cela indique que la fonction a une parabole qui ouvre vers la droite avec l'équation $y = ax$ lorsque x approche l'infini.</p> Signup and view all the answers

<p>Cela signifie que la fonction possède une parabole qui ouvre vers la gauche avec l'équation $y = ax$ lorsque x approche de l'infini négatif.</p> Signup and view all the answers

<p>Une parabole s'ouvrant vers l'axe horizontal se produit si $ ext{lim}_{x o ext{∞}} [f(x) - 0] = 0$.</p> Signup and view all the answers

<p>Si $ ext{lim}_{x o ext{∞}} [f(x) - 0] = 0$, la fonction a une parabole qui ouvre vers l'axe vertical.</p> Signup and view all the answers

<p>Il est important de vérifier les limites des deux côtés pour assurer que la fonction s'approche de l'infini au point a, ce qui confirmera l'existence de l'asymptote.</p> Signup and view all the answers

A horizontal line that the function approaches as x approaches positive or negative infinity.

A vertical line that the function approaches, but never crosses, as x approaches a specific value.

A slanted line that a function approaches as x approaches positive or negative infinity.

The function approaches a parabola opening to the right as x approaches positive infinity.

The function approaches a parabola opening to the left as x approaches negative infinity

The value that a function approaches as x gets very large or very small.

Must be taken from both sides (left and right) to establish the nature of the Vertical Asymptote.

The analysis of how a function behaves at different values of x. This includes analyzing horizontal and vertical asymptotes, as well as branches based on limits.

A horizontal line y = a; a function approaches as x approaches positive or negative infinity

A vertical line x = a; function approaches infinity or negative infinity as x approaches 'a' from both sides

A slanted line y = ax + b; the function approaches as x approaches positive or negative infinity

The function approaches a parabola that opens to the right as x approaches infinity

The function approaches a parabola that opens to the left as x approaches negative infinity

The value a function approaches as x gets very large or very small

Must be taken from both sides (left and right) to ensure the vertical asymptote exists

Examining limit behavior of function, including asymptotes (horizontal, vertical, slanted), and branch directions