Free Grade 3 Key Vocabulary of Introducing Function Notation Techniques: Worked Examples Lessons
Free Grade 3 lessons for Key Vocabulary of Introducing Function Notation Techniques: Worked Examples: 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.
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35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain key vocabulary of introducing function notation techniques: worked examples
Explain key vocabulary of introducing function notation techniques: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate key vocabulary of introducing function notation techniques: worked examples
Calculate key vocabulary of introducing function notation techniques: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare key vocabulary of introducing function notation techniques: worked examples
Compare key vocabulary of introducing function notation techniques: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify key vocabulary of introducing function notation techniques: worked examples
Justify key vocabulary of introducing function notation techniques: worked examples 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 Key Vocabulary of Introducing Function Notation Techniques: Worked Examples 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) = 2x − 7. Find f(1).[1]
- 2.f(x) = 3x + 5. Find f(-4).[1]
- 3.f(x) = 2x − 3. Find f(4).[1]
- 4.f(x) = 2x + 7. Find f(6).[1]
- 5.f(x) = 4x − 1. Find f(-4).[2]
- 6.f(x) = 6x − 5. Find f(-3).[2]
- 7.f(x) = 3x + 8. Find f(6).[2]
- 8.f(x) = 6x + 6. Find f(-1).[2]
- 9.f(x) = 2x − 8. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 5x − 6. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 2x + 7. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x − 5. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -5
Replace x with 1: 2 × 1 − 7. = -5
2. -7
Replace x with -4: 3 × (-4) + 5. = -7
3. 5
Replace x with 4: 2 × 4 − 3. = 5
4. 19
Replace x with 6: 2 × 6 + 7. = 19
5. -17
Replace x with -4: 4 × (-4) − 1. = -17
6. -23
Replace x with -3: 6 × (-3) − 5. = -23
7. 26
Replace x with 6: 3 × 6 + 8. = 26
8. 0
Replace x with -1: 6 × (-1) + 6. = 0
9. f⁻¹(x) = (x + 8) / 2
Write y = 2x − 8 and swap x and y. Rearrange for y: y = (x + 8) / 2.
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 − 7) / 2
Write y = 2x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 2.
12. f⁻¹(x) = (x + 5) / 4
Write y = 4x − 5 and swap x and y. Rearrange for y: y = (x + 5) / 4.
Worked examples
f(x) = 6x + 3. Find f(2).
- Replace x with 2: 6 × 2 + 3.
- = 15
- Answer: 15
f(x) = 5x + 6. Find f(6).
- Replace x with 6: 5 × 6 + 6.
- = 36
- Answer: 36
f(x) = 2x − 4. Find the inverse f⁻¹(x).
- Write y = 2x − 4 and swap x and y.
- Rearrange for y: y = (x + 4) / 2.
- Answer: f⁻¹(x) = (x + 4) / 2
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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