Name: graphing inequality solution ranges
Uploaded: 2025-11-26T05:44:15.000Z
Duration: 1 min 24 s
Channel: JoVE

La résolution graphique des inégalités implique la sélection des valeurs x, le calcul des valeurs y correspondantes à l’aide de la fonction et le tracé du graphique.Ce graphique montre la région mettant en évidence les valeurs x qui satisfont l’inégalité. Sur la même grille, tracez une autre fonction d’inégalité et ombrez le côté de la ligne de démarcation où l’inégalité est vraie.Les valeurs x dans la région qui se chevauche représentent la solution de l’inéquation.Pour une fonction quadratique, la partie ombrée du graphique montre la solution lorsque l’inégalité est supérieure ou égale à. De même, lorsque l’inégalité est inférieure ou égale à, la solution correspond à la région non ombrée du graphique.Lorsqu’une inégalité quadratique est comparée à une fonction linéaire, les deux graphiques sont tracés sur le même plan de coordonnées. Les graphiques se coupent en points. Ces valeurs x marquent les limites de l’ensemble de solutions, indiquant où se trouve la parabole au-dessus ou sur la droite.La méthode graphique de résolution des inégalités est utile dans des domaines tels que la finance, où les dépenses mensuelles peuvent être comparées au budget. La zone ombrée indique que les dépenses restent en dessous de la ligne budgétaire.

résolution graphique des inégalités

Solving Inequalities Graphically

R&#233;soudre graphiquement des in&#233;galit&#233;s consiste &#224; utiliser une approche visuelle pour d&#233;terminer o&#249; une expression math&#233;matique v&#233;rifie une condition donn&#233;e, par exemple, &#234;tre sup&#233;rieure ou inf&#233;rieure &#224; une autre valeur. En examinant la position de la courbe repr&#233;sentative par rapport &#224; l&#8217;axe des abscisses ou &#224; une autre courbe, il devient possible d&#8217;identifier l&#8217;intervalle de valeurs de x qui v&#233;rifient l&#8217;in&#233;galit&#233;. Cette m&#233;thode offre une compr&#233;hension intuitive des intervalles de solutions en montrant o&#249; l&#8217;in&#233;galit&#233; est v&#233;rifi&#233;e.
La r&#233;solution graphique des in&#233;galit&#233;s consiste &#224; tracer les fonctions pertinentes et &#224; identifier les intervalles o&#249; la condition d&#8217;in&#233;galit&#233; est v&#233;rifi&#233;e. Pour une in&#233;galit&#233; quadratique telle que x^2 - 4x + 2 &lt; 0, on trace la fonction y = x^2 - 4x + 2. La solution est l&#8217;ensemble des valeurs de x pour lesquelles la courbe se situe sous l&#8217;axe des abscisses, ce qui correspond &#224; l&#8217;intervalle o&#249; l&#8217;in&#233;galit&#233; est v&#233;rifi&#233;e.
Pour les in&#233;galit&#233;s entre deux fonctions, telles que x^3 - 4x^2 + 8 &#8805; -8, les fonctions y_1 = x^3 - 4x^2 + 8 et y_2 = -8 sont repr&#233;sent&#233;es graphiquement. La solution est constitu&#233;e de toutes les valeurs de x pour lesquelles y_1 &#8805; y_2, ce qui signifie que la courbe repr&#233;sentative de y_1 se situe sur ou au-dessus de la courbe repr&#233;sentative de y_2.
Les m&#233;thodes graphiques permettent d&#8217;identifier rapidement les intervalles de solutions et renseignent sur le comportement de la fonction.

Résolution graphique des inégalités

R&#233;soudre graphiquement des in&#233;galit&#233;s consiste &#224; utiliser une approche visuelle pour d&#233;terminer o&#249; une expression ...

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JoVE Core

Math Fundamentals

Unit

Coordinates and Graphs

KEY TERMS AND CONCEPTS

graphing inequality solution ranges

Graphing inequality solution ranges gives a visual way to find the x-values that make an inequality true. Students look at where a graph sits compared with the x-axis or with another graph. This shows the interval where the condition is satisfied.

For a quadratic inequality, the first step is to plot the related function. For example, with x² − 4x + 2 &lt; 0, graph y = x² − 4x + 2. The solution is the set of x-values where the curve lies below the x-axis.

Inequalities can also compare two functions. For x³ − 4x² + 8 ≥ −8, graph y₁ = x³ − 4x² + 8 and y₂ = −8. The answer includes all x-values where y₁ is on or above y₂. Graphical methods make these solution intervals easy to spot and help show the shape of the function.

Graphing Inequality Solution Ranges

coordinate plane

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The Cartesian coordinate plane is used to find and plot points in two dimensions. It is made of two number lines that cross at right angles. The horizontal line is the x-axis, and the vertical line is the y-axis. Their meeting point is the origin, where both values are zero. The axes divide the plane into four quadrants. These quadrants are labeled in a counterclockwise direction, starting from the upper right. Every point on the plane is written as an ordered pair. The first number is the...

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Finding Distance on a Coordinate Plane

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the midpoint formula

Finding the Center of a Line Segment

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Plotting Two-Variable Equations with Tables

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Ellipse Symmetry at the Origin

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Graphing Equations to Find Intercepts

Graphing equations helps students find intercepts and solutions on the coordinate plane. It gives a visual way to solve equations and understand how a function behaves. To use this method, write the equation in the form y = f(x). The solution to the original equation is the x-value where the graph crosses the x-axis. At that point, f(x) = 0. For example, the linear equation 2x - 4 = 0 can be written as y = 2x - 4. When this function is graphed, it has one x-intercept at x = 2, and that is the...

solving inequalities graphically

Graphing inequality solution ranges gives a visual way to find the x-values that make an inequality true. Students look at where a graph sits compared with the x-axis or with another graph. This shows the interval where the condition is satisfied. For a quadratic inequality, the first step is to plot the related function. For example, with x² − 4x + 2 &lt; 0, graph y = x² − 4x + 2. The solution is the set of x-values where the curve lies below the x-axis. Inequalities can also compare two...

key terms and concepts

Use graphs to find the x-values that satisfy inequalities. Learn how to solve quadratic and two-function inequalities by checking where curves lie on the graph.

Graphing Inequality Solution Ranges | JoVE K12

The JoVE Math Fundamentals collection is designed to build a deep and comprehensive understanding of essential mathematics. Covering the foundations of algebra, geometry, trigonometry, and analytic reasoning, this course establishes a strong base for future studies. The collection connects core mathematical concepts with real-world practice, equipping learners to solve complex problems, master problem-solving skills, and apply abstract ideas.

math fundamentals

Graphing Inequality Solution Ranges

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