Free Grade 3 What is Working with Introducing Function Notation Essentials Worksheets
Free Grade 3 worksheets for What is Working with Introducing 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify what is working with introducing function notation essentials
Identify what is working with introducing function notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain what is working with introducing function notation essentials
Explain what is working with introducing function notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate what is working with introducing function notation essentials
Calculate what is working with introducing function notation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare what is working with introducing function notation essentials
Compare what is working with introducing 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 What is Working with Introducing 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) = 2x − 6. Find f(3).[1]
- 2.f(x) = 6x + 5. Find f(2).[1]
- 3.f(x) = 3x + 3. Find f(5).[1]
- 4.f(x) = 6x − 5. Find f(4).[1]
- 5.f(x) = 3x + 0. Find f(1).[2]
- 6.f(x) = 5x + 2. Find f(-4).[2]
- 7.f(x) = 2x − 2. Find f(1).[2]
- 8.f(x) = 2x + 6. Find f(3).[2]
- 9.f(x) = 5x + 4. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 3x + 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 4x − 7. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x + 8. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 0
Replace x with 3: 2 × 3 − 6. = 0
2. 17
Replace x with 2: 6 × 2 + 5. = 17
3. 18
Replace x with 5: 3 × 5 + 3. = 18
4. 19
Replace x with 4: 6 × 4 − 5. = 19
5. 3
Replace x with 1: 3 × 1 + 0. = 3
6. -18
Replace x with -4: 5 × (-4) + 2. = -18
7. 0
Replace x with 1: 2 × 1 − 2. = 0
8. 12
Replace x with 3: 2 × 3 + 6. = 12
9. f⁻¹(x) = (x − 4) / 5
Write y = 5x + 4 and swap x and y. Rearrange for y: y = (x − 4) / 5.
10. f⁻¹(x) = (x − 8) / 3
Write y = 3x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 3.
11. f⁻¹(x) = (x + 7) / 4
Write y = 4x − 7 and swap x and y. Rearrange for y: y = (x + 7) / 4.
12. f⁻¹(x) = (x − 8) / 6
Write y = 6x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 6.
Worked examples
f(x) = 5x + 4. Find f(3).
- Replace x with 3: 5 × 3 + 4.
- = 19
- Answer: 19
f(x) = 4x + 8. Find f(4).
- Replace x with 4: 4 × 4 + 8.
- = 24
- Answer: 24
f(x) = 3x − 5. Find the inverse f⁻¹(x).
- Write y = 3x − 5 and swap x and y.
- Rearrange for y: y = (x + 5) / 3.
- Answer: f⁻¹(x) = (x + 5) / 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 What is Working with Introducing Function Notation Essentials worksheet really free?
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- What should a learner already know before this?
- Start with Rules and Methods in Introducing Function Notation Essentials. 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 What is Working with Introducing Function Notation Essentials?
- Move on to Working with Introducing Function Notation Essentials: Step-by-step Method, Working with Introducing Function Notation Essentials: Worked Examples, Working with Introducing Function Notation Essentials: Visual Models, Working with Introducing Function Notation Essentials: Common Mistakes, which build directly on this idea.
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