تدرب وحل المسائل في الدوال - كتاب الرياضيات - الصف 12 - الفصل 1 - المملكة العربية السعودية

--- SECTION: تدرب وحل المسائل --- تدرب وحل المسائل اكتب كل مجموعة مما يأتي، باستعمال الصفة المميزة للمجموعة، وباستعمال رمز الفترة إن أمكن: (المثالان 1, 2)--- SECTION: 1 --- 1 x > 50--- SECTION: 2 --- 2 x < -13--- SECTION: 3 --- 3 x ≤ -4--- SECTION: 4 --- 4 {-3, -2, -1, ...}--- SECTION: 5 --- 5 -31 < x ≤ 64--- SECTION: 6 --- 6 x ≥ 21 أو x < -19--- SECTION: 7 --- 7 x ≥ 61 أو x ≤ 67--- SECTION: 8 --- 8 x ≥ 86 أو x ≤ -45--- SECTION: 9 --- 9 المضاعفات الموجبة للعدد 10--- SECTION: 10 --- 10 x ≥ 32في كل علاقة مما يأتي، حدد ما إذا كانت y تمثل دالة في x أم لا: (مثال 3)--- SECTION: 11 --- 11 المتغير المستقل x يمثل رقم الحساب في البنك، والمتغير y يمثل الرصيد في الحساب.--- SECTION: 13 --- 13 1/x = y--- SECTION: 14 --- 14 x² = y + 2--- SECTION: 15 --- 15 √(48y) = x--- SECTION: 16 --- 16 x/y = y - 6أوجد قيم كل دالة من الدوال الآتية: (مثال 4)--- SECTION: 19 --- 19 g(x) = 2x² + 18x - 14 a g(9) b g(3x) c g(1 + 5m)--- SECTION: 20 --- 20 h(y) = -3y³ - 6y + 9 a h(4) b h(-2y) c h(5b + 3)--- SECTION: 21 --- 21 f(t) = (4t + 11) / (3t² + 5t + 1) a f(-6) b f(4t) c f(3 - 2a)--- SECTION: 22 --- 22 g(x) = (3x³) / (x² + x - 4) a g(-2) b g(5x) c g(8 - 4b)--- SECTION: 23 --- 23 g(m) = 3 + √(m² - 4) a g(-2) b g(3m) c g(4m - 2)--- SECTION: 24 --- 24 t(x) = 5√(6x²) a t(-4) b t(2x) c t(7 + n)--- SECTION: 25 --- 25 مبيعات: قدرت مبيعات شركة للسيارات خلال خمس سنوات بالدالة: f(t) = 24t² - 93t + 78، حيث t الزمن بالسنوات، وكانت المبيعات الفعلية موضحة في الجدول المجاور. (مثال 4) a أوجد (1)f. b أوجد (5)f. c هل تعتقد أن القاعدة (t)f أكثر دقة في السنة الأولى، أم في السنة الأخيرة؟ برر إجابتك.حدد مجال كل دالة مما يأتي: (مثال 5)--- SECTION: 26 --- 26 f(x) = (8x + 12) / (x² + 5x + 4)--- SECTION: 27 --- 27 g(x) = (x + 1) / (x² - 3x - 40)--- SECTION: 28 --- 28 g(a) = √(1 + a²)--- SECTION: 29 --- 29 h(x) = √(6 - x²)--- SECTION: 30 --- 30 f(a) = (5a) / √(4a - 1)--- SECTION: 31 --- 31 f(x) = 2/x + 4/(x + 1)--- SECTION: 32 --- 32 فيزياء: يعطى زمن الدورة T لبندول ساعة بالصيغة T = 2π√(ℓ/9.8)، حيث ℓ طول البندول، فهل تمثل T دالة في ℓ؟ إذا كانت كذلك فحدد مجالها، وإذا لم تكن دالة فبين السبب. (مثال 5)الدرس 1-1: الدوال2025 - 1447--- VISUAL CONTEXT --- **TABLE**: Untitled Description: Table showing x and y values for a relation, associated with question 12. Table Structure: Headers: x | y Rows: Row 1: 0.01 | 423 Row 2: 0.04 | 449 Row 3: 0.04 | 451 Row 4: 0.07 | 466 Row 5: 0.08 | 478 Row 6: 0.09 | 482 Data: Pairs of x and y values are provided. Note that x=0.04 corresponds to two different y values (449 and 451). Context: Used to determine if the relation represented by the data is a function.**GRAPH**: Untitled Description: A Cartesian coordinate graph showing a circle centered at the origin, associated with question 17. This graph represents a relation, not a function. X-axis: x Y-axis: y Data: A circle is plotted on the graph. The circle appears to have a radius of approximately 3 units, passing through (±3, 0) and (0, ±3). Key Values: center: (0,0), estimated radius: 3 units Context: Used to visually determine if the graphed relation is a function (fails the vertical line test). (Note: Some details are estimated)**GRAPH**: Untitled Description: A Cartesian coordinate graph showing a V-shaped curve, typical of an absolute value function, centered at the origin, associated with question 18. This graph represents a function. X-axis: x Y-axis: y Data: A V-shaped graph with its vertex at the origin (0,0). The branches extend upwards, passing through points like (±2, 2) and (±4, 4). Key Values: vertex: (0,0), points: (±2, 2), (±4, 4) Context: Used to visually determine if the graphed relation is a function (passes the vertical line test). (Note: Some details are estimated)**TABLE**: المبيعات Description: Table showing actual sales data in millions of Riyals over five years, associated with question 25. Table Structure: Headers: السنة | المبيعات بملايين الريالات Rows: Row 1: 1 | 1 Row 2: 2 | 3 Row 3: 3 | 14 Row 4: 4 | 74 Row 5: 5 | 219 Data: Sales figures increase significantly each year, from 1 million in year 1 to 219 million in year 5. Context: Provides empirical data to compare against a mathematical model (function f(t)) for sales prediction.**IMAGE**: Untitled Description: An illustration of a pendulum clock, highlighting the length (ℓ) of the pendulum and its period (T). This image is associated with the physics problem in question 32. Context: Visual aid for a physics problem that asks about the relationship between the pendulum's period and its length, and whether the period is a function of the length.