Free Grade 3 What is Introduction to Function Notation in Context Techniques — Reasoning Lessons
Free Grade 3 lessons for What is Introduction to Function Notation in Context Techniques — Reasoning: 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 what is introduction to function notation in context techniques — reasoning
Identify what is introduction to function notation in context techniques — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain what is introduction to function notation in context techniques — reasoning
Explain what is introduction to function notation in context techniques — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate what is introduction to function notation in context techniques — reasoning
Calculate what is introduction to function notation in context techniques — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare what is introduction to function notation in context techniques — reasoning
Compare what is introduction to function notation in context techniques — reasoning 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 What is Introduction to Function Notation in Context Techniques — Reasoning 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) = 3x + 6. Find f(0).[1]
- 2.f(x) = 6x − 4. Find f(6).[1]
- 3.f(x) = 4x − 2. Find f(4).[1]
- 4.f(x) = 3x − 6. Find f(0).[1]
- 5.f(x) = 6x − 4. Find f(-4).[2]
- 6.f(x) = 4x − 6. Find f(-4).[2]
- 7.f(x) = 5x + 1. Find f(-4).[2]
- 8.f(x) = 6x + 3. Find f(6).[2]
- 9.f(x) = 4x − 3. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 5x + 6. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x + 4. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x − 6. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 6
Replace x with 0: 3 × 0 + 6. = 6
2. 32
Replace x with 6: 6 × 6 − 4. = 32
3. 14
Replace x with 4: 4 × 4 − 2. = 14
4. -6
Replace x with 0: 3 × 0 − 6. = -6
5. -28
Replace x with -4: 6 × (-4) − 4. = -28
6. -22
Replace x with -4: 4 × (-4) − 6. = -22
7. -19
Replace x with -4: 5 × (-4) + 1. = -19
8. 39
Replace x with 6: 6 × 6 + 3. = 39
9. f⁻¹(x) = (x + 3) / 4
Write y = 4x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 4.
10. f⁻¹(x) = (x − 6) / 5
Write y = 5x + 6 and swap x and y. Rearrange for y: y = (x − 6) / 5.
11. f⁻¹(x) = (x − 4) / 6
Write y = 6x + 4 and swap x and y. Rearrange for y: y = (x − 4) / 6.
12. f⁻¹(x) = (x + 6) / 3
Write y = 3x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 3.
Worked examples
f(x) = 6x + 7. Find f(-3).
- Replace x with -3: 6 × (-3) + 7.
- = -11
- Answer: -11
f(x) = 3x + 6. Find f(-3).
- Replace x with -3: 3 × (-3) + 6.
- = -3
- Answer: -3
f(x) = 5x + 5. Find the inverse f⁻¹(x).
- Write y = 5x + 5 and swap x and y.
- Rearrange for y: y = (x − 5) / 5.
- Answer: f⁻¹(x) = (x − 5) / 5
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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- Start with What is Introduction to Function Notation in Context Techniques — Application, What is Introduction to Function Notation in Context Techniques — Understanding, Function Notation in Context Essentials. Each one has its own free lesson, worksheet and quiz.
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- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
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- Move on to What is Introduction to Function Notation in Context Techniques — Mastery, Introduction to Function Notation in Context Techniques: Step-by-step Method, Introduction to Function Notation in Context Techniques: Worked Examples, Introduction to Function Notation in Context Techniques: Visual Models, which build directly on this idea.
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