Mathematics Class 10 Chapter 6: Functions and Graphs

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• Class 10
• Mathematics
• Chapter 6
• Book pages 115-139
• FBISE SSC-II

Chapter summary

Chapter 6 of Mathematics for Class 10 is called "Functions and Graphs". It covers 17 learning outcomes of the Federal Board syllabus. You will learn to: recognize notation and determine the value of a function; identify types of functions (into, onto, one-to-one, injective, surjective and bijective) by using Venn diagrams. Parhayi.com has 360 MCQs, 34 short questions and 15 long questions for this chapter.

Topics in this chapter

• Recognize notation and determine the value of a function
• Identify types of functions (into, onto, one-to-one, injective, surjective and bijective) by using Venn diagrams
• Explain operations on, and compositions of, functions
• Find the inverse of a given function
• Formulate composite functions as defined by (g o f)(x) = g(f(x))
• Apply concepts from functions to real world problems (such as finance, transportation, and sales)
• Plot graphs of constant function, identity function, linear function and absolute valued functions
• Solve absolute value equations and inequalities in one variable and express the solution as a range of values on a number line
• Apply concepts of absolute valued functions to real-world problems (such as to calculate energy wave, magnitude and distance)
• Apply concepts from functions to real world problems (such as finance, transportation, and sales)
• Draw graphs of functions of the form y = ax^n (including the sums of few of these taking n as a rational number)
• Solve a system of one linear and one quadratic equation graphically and interpret the solution
• Discover exponential growth/decay of a practical phenomenon through its graph
• Identify, sketch and interpret graphs of the linear functions
• Identify, sketch and interpret graphs of the non-linear functions such as quadratic, cubic, reciprocal, and exponential functions
• Sketch graph of the function y = x^n where n is a positive integer, negative integer, rational number for x > 0
• Apply concepts of sketching and interpreting graph to real life problems (such as in tax payment, income and salary problems and cost and profit analy

Sample questions

Try these questions from the chapter. The answers are for Premium students.

1. If \(f(x)=2x+1\) and \(g(x)=x-3\), find \(f(g(x))\) and \(g(f(x))\). (4 marks)
2. Find the inverse of \(f(x)=3x-7\) and verify that \(f(f^{-1}(x))=x\). (4 marks)
3. Find the domain of (i) \(f(x)=\dfrac1{x-4}\) (ii) \(g(x)=\sqrt{x-2}\). (3 marks)

What Premium gives you in this chapter

• 360 MCQs with answers and explanations
• 34 short questions with full answers
• 15 long questions with answers
• 17 Learn cards
• 9 Activities and games
• chapter tests that show your weak topics

Mathematics grows step by step. Read the rule, study one worked example, then solve similar questions yourself and check every step.