Free Grade 3 Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application Worksheets
Free Grade 3 worksheets for Rules and Methods in Function Notation in Context Techniques: Common Mistakes — 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify rules and methods in function notation in context techniques: common mistakes — application
Identify rules and methods in function notation in context techniques: common mistakes — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain rules and methods in function notation in context techniques: common mistakes — application
Explain rules and methods in function notation in context techniques: common mistakes — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate rules and methods in function notation in context techniques: common mistakes — application
Calculate rules and methods in function notation in context techniques: common mistakes — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare rules and methods in function notation in context techniques: common mistakes — application
Compare rules and methods in function notation in context techniques: common mistakes — 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 Rules and Methods in Function Notation in Context Techniques: Common Mistakes — 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) = 2x − 1. Find f(-3).[1]
- 2.f(x) = 5x + 5. Find f(4).[1]
- 3.f(x) = 2x + 3. Find f(3).[1]
- 4.f(x) = 6x − 5. Find f(2).[1]
- 5.f(x) = 5x + 1. Find f(-2).[2]
- 6.f(x) = 5x + 8. Find f(-1).[2]
- 7.f(x) = 2x + 3. Find f(2).[2]
- 8.f(x) = 6x − 4. Find f(-4).[2]
- 9.f(x) = 4x + 0. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x − 1. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 5x + 7. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x + 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -7
Replace x with -3: 2 × (-3) − 1. = -7
2. 25
Replace x with 4: 5 × 4 + 5. = 25
3. 9
Replace x with 3: 2 × 3 + 3. = 9
4. 7
Replace x with 2: 6 × 2 − 5. = 7
5. -9
Replace x with -2: 5 × (-2) + 1. = -9
6. 3
Replace x with -1: 5 × (-1) + 8. = 3
7. 7
Replace x with 2: 2 × 2 + 3. = 7
8. -28
Replace x with -4: 6 × (-4) − 4. = -28
9. f⁻¹(x) = (x − 0) / 4
Write y = 4x + 0 and swap x and y. Rearrange for y: y = (x − 0) / 4.
10. f⁻¹(x) = (x + 1) / 2
Write y = 2x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 2.
11. f⁻¹(x) = (x − 7) / 5
Write y = 5x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 5.
12. f⁻¹(x) = (x − 3) / 4
Write y = 4x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 4.
Worked examples
f(x) = 2x + 3. Find f(4).
- Replace x with 4: 2 × 4 + 3.
- = 11
- Answer: 11
f(x) = 2x + 6. Find f(-3).
- Replace x with -3: 2 × (-3) + 6.
- = 0
- Answer: 0
f(x) = 6x + 0. Find the inverse f⁻¹(x).
- Write y = 6x + 0 and swap x and y.
- Rearrange for y: y = (x − 0) / 6.
- Answer: f⁻¹(x) = (x − 0) / 6
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.
Every free resource for Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application
One concept, one ecosystem — all of it free.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application 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 Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Understanding, Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Recognition, Rules and Methods in Function Notation in Context Techniques: Visual Models. 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 Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application?
- Move on to Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Reasoning, Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Mastery, What is Rules and Methods in Function Notation in Context Techniques, Rules and Methods in Function Notation in Context Techniques: Step-by-step Method, which build directly on this idea.
Related resources
- Free Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application quizzes
- Free Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application flashcards
- Free Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application lessons
- Free Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application lesson plans
- Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application in the knowledge graph
- Free AI Tutor
Stuck on Rules and Methods in Function Notation in Context Techniques: Common Mistakes — Application? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor