General Mathematics · 2nd secondary · First Term

Real Functions and Graphing Curves — Real functions

About this lesson

This unit introduces real functions, focusing on their definition, representation, and analysis. It covers the concept of a real function (domain and co-domain as real numbers or subsets), the vertical line test for identifying functions from graphs, and the piecewise-defined function (a function with different rules for different subsets of its domain). Students learn to identify the domain and range of real functions from their graphs or algebraic rules, including cases with polynomial, rational, and radical expressions. The unit also covers operations on functions (addition, subtraction, multiplication, and division), including how to determine the domain of the resulting function. Examples and exercises involve graphing linear and piecewise functions, deducing domain and range from graphs, and solving problems related to real-world contexts like gas consumption and distribution charges.

Main topics in this lesson

  • Real functions and their properties
  • Vertical line test
  • Piecewise-defined functions
  • Identifying domain and range
  • Operations on functions

Key terms and vocabulary

  • Real function
  • Domain
  • Co-domain
  • Range
  • Vertical line test
  • Piecewise-defined function
  • Arrow diagram
  • Cartesian diagram
  • Rule of the function
  • Operations on functions
  • Zeros of a function

Questions and answers on Real Functions and Graphing Curves — Real functions - practice and revision

Multiple choice questions on this lesson in General Mathematics for 2nd secondary, First Term, with practice exercises for revision and exam preparation.

1

إذا كانت الدالة ق(س) = ٢س + ١، فإن قيمة س التي تجعل ق(س) = ٩ هي:

  • 1 ٤
  • 2 ٥
  • 3 ٣
  • 4 ٨
2

إذا كان ق(س) = ٣س + ١، هـ(س) = س − ٢، فإن (ق − هـ)(س) تساوي:

  • 1 ٢س + ٣
  • 2 ٢س − ١
  • 3 ٤س − ١
  • 4 ٢س − ٣
3

مجال الدالة ق(س) = ١/(س² − ٤) هو:

  • 1 ح − {٢، −٢}
  • 2 ح − {٢}
  • 3 ح − {٤}
  • 4 ح
4

إذا كان ق(س) = ٥س − ١، فإن ق(٠) تساوي:

  • 1 −١
  • 2 ١
  • 3 ٠
  • 4 ٥
5

لمعرفة ما إذا كان التمثيل البياني يمثل دالة حقيقية أم لا نستخدم:

  • 1 اختبار الخط الرأسي
  • 2 اختبار الخط الأفقي
  • 3 اختبار الخط المائل
  • 4 اختبار نقطة الأصل
6

أصفار الدالة ق(س) = ٢س − ٦ هي:

  • 1 ٣
  • 2 −٣
  • 3 ٦
  • 4 ٢

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