Free Grade 3 Introduction to Working with Function Notation Techniques: Real-life Applications Lessons
Free Grade 3 lessons for Introduction to Working with Function Notation Techniques: Real-life Applications: 12 real questions with a full answer key and worked solutions. A function is a rule that turns an input into an output. The inverse function reverses it.
Free
Higher
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introduction to working with function notation techniques: real-life applications
Identify introduction to working with function notation techniques: real-life applications accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introduction to working with function notation techniques: real-life applications
Explain introduction to working with function notation techniques: real-life applications accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to working with function notation techniques: real-life applications
Calculate introduction to working with function notation techniques: real-life applications accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to working with function notation techniques: real-life applications
Compare introduction to working with function notation techniques: real-life applications accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introduction to Working with Function Notation Techniques: Real-life Applications works
A function is a rule that turns an input into an output. The inverse function reverses it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.f(x) = 5x − 7. Find f(-3).[1]
- 2.f(x) = 6x − 2. Find f(-3).[1]
- 3.f(x) = 3x − 2. Find f(6).[1]
- 4.f(x) = 5x − 1. Find f(4).[1]
- 5.f(x) = 3x − 7. Find f(-1).[2]
- 6.f(x) = 4x − 4. Find f(-2).[2]
- 7.f(x) = 6x − 8. Find f(1).[2]
- 8.f(x) = 2x + 0. Find f(6).[2]
- 9.f(x) = 2x − 2. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 6x − 1. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 2x − 5. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x + 8. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -22
Replace x with -3: 5 × (-3) − 7. = -22
2. -20
Replace x with -3: 6 × (-3) − 2. = -20
3. 16
Replace x with 6: 3 × 6 − 2. = 16
4. 19
Replace x with 4: 5 × 4 − 1. = 19
5. -10
Replace x with -1: 3 × (-1) − 7. = -10
6. -12
Replace x with -2: 4 × (-2) − 4. = -12
7. -2
Replace x with 1: 6 × 1 − 8. = -2
8. 12
Replace x with 6: 2 × 6 + 0. = 12
9. f⁻¹(x) = (x + 2) / 2
Write y = 2x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 2.
10. f⁻¹(x) = (x + 1) / 6
Write y = 6x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 6.
11. f⁻¹(x) = (x + 5) / 2
Write y = 2x − 5 and swap x and y. Rearrange for y: y = (x + 5) / 2.
12. f⁻¹(x) = (x − 8) / 4
Write y = 4x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 4.
Worked examples
f(x) = 6x − 3. Find f(5).
- Replace x with 5: 6 × 5 − 3.
- = 27
- Answer: 27
f(x) = 2x − 4. Find f(-3).
- Replace x with -3: 2 × (-3) − 4.
- = -10
- Answer: -10
f(x) = 6x + 5. Find the inverse f⁻¹(x).
- Write y = 6x + 5 and swap x and y.
- Rearrange for y: y = (x − 5) / 6.
- Answer: f⁻¹(x) = (x − 5) / 6
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads f(3) as f × 3.
Correction: f(3) means 'put 3 into the rule'.
Reverses operations in the wrong order for the inverse.
Correction: Undo the last step first.
Teacher tips
- · Use function machines before notation.
Parent tips
- · Play 'guess my rule' with numbers.
Real-life applications
- · Converting temperatures, phone-plan costs.
Assessment objectives
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Frequently asked
- Is this Grade 3 Introduction to Working with Function Notation Techniques: Real-life Applications lesson really free?
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- What should a learner already know before this?
- Start with Introduction to Working with Function Notation Techniques: Common Mistakes, Introduction to Working with Function Notation Techniques: Visual Models, Working with Function Notation Essentials. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introduction to Working with Function Notation Techniques: Real-life Applications?
- Move on to Key Vocabulary of Working with Function Notation Techniques, Rules and Methods in Working with Function Notation Techniques, Working with Working with Function Notation Techniques, Working with Function Notation Techniques in Examinations, which build directly on this idea.
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