Free Grade 3 Working with Introducing Function Notation Essentials: Step-by-step Method — Application Lessons
Free Grade 3 lessons for Working with Introducing Function Notation Essentials: Step-by-step Method — Application: 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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Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with introducing function notation essentials: step-by-step method — application
Explain working with introducing function notation essentials: step-by-step method — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with introducing function notation essentials: step-by-step method — application
Calculate working with introducing function notation essentials: step-by-step method — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with introducing function notation essentials: step-by-step method — application
Compare working with introducing function notation essentials: step-by-step method — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with introducing function notation essentials: step-by-step method — application
Justify working with introducing function notation essentials: step-by-step method — application 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 Working with Introducing Function Notation Essentials: Step-by-step Method — Application 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 + 1. Find f(2).[1]
- 2.f(x) = 3x − 2. Find f(1).[1]
- 3.f(x) = 2x − 2. Find f(-3).[1]
- 4.f(x) = 3x − 8. Find f(3).[1]
- 5.f(x) = 2x + 8. Find f(-4).[2]
- 6.f(x) = 5x + 7. Find f(-3).[2]
- 7.f(x) = 4x + 1. Find f(1).[2]
- 8.f(x) = 4x + 5. Find f(0).[2]
- 9.f(x) = 4x − 6. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 6x − 1. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 5x + 4. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 5x − 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 7
Replace x with 2: 3 × 2 + 1. = 7
2. 1
Replace x with 1: 3 × 1 − 2. = 1
3. -8
Replace x with -3: 2 × (-3) − 2. = -8
4. 1
Replace x with 3: 3 × 3 − 8. = 1
5. 0
Replace x with -4: 2 × (-4) + 8. = 0
6. -8
Replace x with -3: 5 × (-3) + 7. = -8
7. 5
Replace x with 1: 4 × 1 + 1. = 5
8. 5
Replace x with 0: 4 × 0 + 5. = 5
9. f⁻¹(x) = (x + 6) / 4
Write y = 4x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 4.
10. f⁻¹(x) = (x + 1) / 6
Write y = 6x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 6.
11. f⁻¹(x) = (x − 4) / 5
Write y = 5x + 4 and swap x and y. Rearrange for y: y = (x − 4) / 5.
12. f⁻¹(x) = (x + 3) / 5
Write y = 5x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 5.
Worked examples
f(x) = 4x − 4. Find f(5).
- Replace x with 5: 4 × 5 − 4.
- = 16
- Answer: 16
f(x) = 6x − 8. Find f(-3).
- Replace x with -3: 6 × (-3) − 8.
- = -26
- Answer: -26
f(x) = 4x + 2. Find the inverse f⁻¹(x).
- Write y = 4x + 2 and swap x and y.
- Rearrange for y: y = (x − 2) / 4.
- Answer: f⁻¹(x) = (x − 2) / 4
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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