Free Grade 3 Key Vocabulary of Working with Function Notation Essentials Worksheets
Free Grade 3 worksheets for Key Vocabulary of Working with Function Notation Essentials: 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify key vocabulary of working with function notation essentials
Identify key vocabulary of working with function notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain key vocabulary of working with function notation essentials
Explain key vocabulary of working with function notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate key vocabulary of working with function notation essentials
Calculate key vocabulary of working with function notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare key vocabulary of working with function notation essentials
Compare key vocabulary of working with function notation essentials 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 Working with Function Notation Essentials 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 + 2. Find f(-1).[1]
- 2.f(x) = 2x + 7. Find f(1).[1]
- 3.f(x) = 5x − 7. Find f(2).[1]
- 4.f(x) = 3x − 3. Find f(-4).[1]
- 5.f(x) = 3x − 6. Find f(-3).[2]
- 6.f(x) = 3x + 1. Find f(3).[2]
- 7.f(x) = 5x − 1. Find f(2).[2]
- 8.f(x) = 5x + 4. Find f(-3).[2]
- 9.f(x) = 3x + 6. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 6x + 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 4x + 4. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x + 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -4
Replace x with -1: 6 × (-1) + 2. = -4
2. 9
Replace x with 1: 2 × 1 + 7. = 9
3. 3
Replace x with 2: 5 × 2 − 7. = 3
4. -15
Replace x with -4: 3 × (-4) − 3. = -15
5. -15
Replace x with -3: 3 × (-3) − 6. = -15
6. 10
Replace x with 3: 3 × 3 + 1. = 10
7. 9
Replace x with 2: 5 × 2 − 1. = 9
8. -11
Replace x with -3: 5 × (-3) + 4. = -11
9. f⁻¹(x) = (x − 6) / 3
Write y = 3x + 6 and swap x and y. Rearrange for y: y = (x − 6) / 3.
10. f⁻¹(x) = (x − 8) / 6
Write y = 6x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 6.
11. f⁻¹(x) = (x − 4) / 4
Write y = 4x + 4 and swap x and y. Rearrange for y: y = (x − 4) / 4.
12. f⁻¹(x) = (x − 3) / 3
Write y = 3x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 3.
Worked examples
f(x) = 2x − 8. Find f(2).
- Replace x with 2: 2 × 2 − 8.
- = -4
- Answer: -4
f(x) = 4x + 1. Find f(2).
- Replace x with 2: 4 × 2 + 1.
- = 9
- Answer: 9
f(x) = 3x − 7. Find the inverse f⁻¹(x).
- Write y = 3x − 7 and swap x and y.
- Rearrange for y: y = (x + 7) / 3.
- Answer: f⁻¹(x) = (x + 7) / 3
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 Key Vocabulary of Working with Function Notation Essentials worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Introduction to Working with Function Notation Essentials, Introducing Function Notation. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Key Vocabulary of Working with Function Notation Essentials?
- Move on to Rules and Methods in Working with Function Notation Essentials, Working with Working with Function Notation Essentials, Working with Function Notation Essentials in Examinations, Working with Function Notation Techniques, which build directly on this idea.
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