Free Grade 3 Key Vocabulary of Function Notation in Context Common Errors: Worked Examples Worksheets
Free Grade 3 worksheets for Key Vocabulary of Function Notation in Context Common Errors: 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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30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain key vocabulary of function notation in context common errors: worked examples
Explain key vocabulary of function notation in context common errors: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate key vocabulary of function notation in context common errors: worked examples
Calculate key vocabulary of function notation in context common errors: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare key vocabulary of function notation in context common errors: worked examples
Compare key vocabulary of function notation in context common errors: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify key vocabulary of function notation in context common errors: worked examples
Justify key vocabulary of function notation in context common errors: 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 Function Notation in Context Common Errors: 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) = 6x + 3. Find f(3).[1]
- 2.f(x) = 2x + 2. Find f(6).[1]
- 3.f(x) = 4x − 6. Find f(-2).[1]
- 4.f(x) = 2x + 2. Find f(4).[1]
- 5.f(x) = 2x − 6. Find f(-4).[2]
- 6.f(x) = 6x − 5. Find f(3).[2]
- 7.f(x) = 3x − 7. Find f(6).[2]
- 8.f(x) = 2x + 3. Find f(0).[2]
- 9.f(x) = 3x − 2. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 5x − 7. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 2x − 3. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x − 8. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 21
Replace x with 3: 6 × 3 + 3. = 21
2. 14
Replace x with 6: 2 × 6 + 2. = 14
3. -14
Replace x with -2: 4 × (-2) − 6. = -14
4. 10
Replace x with 4: 2 × 4 + 2. = 10
5. -14
Replace x with -4: 2 × (-4) − 6. = -14
6. 13
Replace x with 3: 6 × 3 − 5. = 13
7. 11
Replace x with 6: 3 × 6 − 7. = 11
8. 3
Replace x with 0: 2 × 0 + 3. = 3
9. f⁻¹(x) = (x + 2) / 3
Write y = 3x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 3.
10. f⁻¹(x) = (x + 7) / 5
Write y = 5x − 7 and swap x and y. Rearrange for y: y = (x + 7) / 5.
11. f⁻¹(x) = (x + 3) / 2
Write y = 2x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 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) = 2x + 1. Find f(3).
- Replace x with 3: 2 × 3 + 1.
- = 7
- Answer: 7
f(x) = 3x − 1. Find f(1).
- Replace x with 1: 3 × 1 − 1.
- = 2
- Answer: 2
f(x) = 5x + 1. Find the inverse f⁻¹(x).
- Write y = 5x + 1 and swap x and y.
- Rearrange for y: y = (x − 1) / 5.
- Answer: f⁻¹(x) = (x − 1) / 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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