Free Grade 3 What is Rules and Methods in Introducing Function Notation Common Errors — Application Lessons
Free Grade 3 lessons for What is Rules and Methods in Introducing Function Notation Common Errors — 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.
Free
Stretch
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain what is rules and methods in introducing function notation common errors — application
Explain what is rules and methods in introducing function notation common errors — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate what is rules and methods in introducing function notation common errors — application
Calculate what is rules and methods in introducing function notation common errors — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare what is rules and methods in introducing function notation common errors — application
Compare what is rules and methods in introducing function notation common errors — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify what is rules and methods in introducing function notation common errors — application
Justify what is rules and methods in introducing function notation common errors — 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 What is Rules and Methods in Introducing Function Notation Common Errors — 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 + 3. Find f(0).[1]
- 2.f(x) = 2x − 2. Find f(0).[1]
- 3.f(x) = 2x − 7. Find f(2).[1]
- 4.f(x) = 5x + 4. Find f(0).[1]
- 5.f(x) = 2x + 1. Find f(0).[2]
- 6.f(x) = 2x + 1. Find f(4).[2]
- 7.f(x) = 6x + 1. Find f(0).[2]
- 8.f(x) = 6x − 5. Find f(-4).[2]
- 9.f(x) = 2x + 3. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 5x + 5. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x + 0. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x + 7. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 3
Replace x with 0: 3 × 0 + 3. = 3
2. -2
Replace x with 0: 2 × 0 − 2. = -2
3. -3
Replace x with 2: 2 × 2 − 7. = -3
4. 4
Replace x with 0: 5 × 0 + 4. = 4
5. 1
Replace x with 0: 2 × 0 + 1. = 1
6. 9
Replace x with 4: 2 × 4 + 1. = 9
7. 1
Replace x with 0: 6 × 0 + 1. = 1
8. -29
Replace x with -4: 6 × (-4) − 5. = -29
9. f⁻¹(x) = (x − 3) / 2
Write y = 2x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 2.
10. f⁻¹(x) = (x − 5) / 5
Write y = 5x + 5 and swap x and y. Rearrange for y: y = (x − 5) / 5.
11. f⁻¹(x) = (x − 0) / 3
Write y = 3x + 0 and swap x and y. Rearrange for y: y = (x − 0) / 3.
12. f⁻¹(x) = (x − 7) / 6
Write y = 6x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 6.
Worked examples
f(x) = 5x + 4. Find f(5).
- Replace x with 5: 5 × 5 + 4.
- = 29
- Answer: 29
f(x) = 6x + 1. Find f(6).
- Replace x with 6: 6 × 6 + 1.
- = 37
- Answer: 37
f(x) = 3x − 8. Find the inverse f⁻¹(x).
- Write y = 3x − 8 and swap x and y.
- Rearrange for y: y = (x + 8) / 3.
- Answer: f⁻¹(x) = (x + 8) / 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
How mastery is evidenced, and which standards it maps to.
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