Free Grade 3 Composite Functions in Context Worksheets
Free Grade 3 worksheets for Composite Functions in Context: 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
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify composite functions in context
Identify composite functions in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain composite functions in context
Explain composite functions in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate composite functions in context
Calculate composite functions in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare composite functions in context
Compare composite functions in context 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 Composite Functions in Context 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(-2).[1]
- 2.f(x) = 4x − 7. Find f(6).[1]
- 3.f(x) = 4x + 6. Find f(-4).[1]
- 4.f(x) = 2x − 4. Find f(-3).[1]
- 5.f(x) = 6x + 3. Find f(-1).[2]
- 6.f(x) = 5x − 3. Find f(-3).[2]
- 7.f(x) = 6x − 1. Find f(0).[2]
- 8.f(x) = 3x + 7. Find f(-3).[2]
- 9.f(x) = 4x − 2. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x + 7. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 4x − 5. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 2x + 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -10
Replace x with -2: 6 × (-2) + 2. = -10
2. 17
Replace x with 6: 4 × 6 − 7. = 17
3. -10
Replace x with -4: 4 × (-4) + 6. = -10
4. -10
Replace x with -3: 2 × (-3) − 4. = -10
5. -3
Replace x with -1: 6 × (-1) + 3. = -3
6. -18
Replace x with -3: 5 × (-3) − 3. = -18
7. -1
Replace x with 0: 6 × 0 − 1. = -1
8. -2
Replace x with -3: 3 × (-3) + 7. = -2
9. f⁻¹(x) = (x + 2) / 4
Write y = 4x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 4.
10. f⁻¹(x) = (x − 7) / 2
Write y = 2x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 2.
11. f⁻¹(x) = (x + 5) / 4
Write y = 4x − 5 and swap x and y. Rearrange for y: y = (x + 5) / 4.
12. f⁻¹(x) = (x − 3) / 2
Write y = 2x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 2.
Worked examples
f(x) = 3x + 1. Find f(-4).
- Replace x with -4: 3 × (-4) + 1.
- = -11
- Answer: -11
f(x) = 5x − 8. Find f(3).
- Replace x with 3: 5 × 3 − 8.
- = 7
- Answer: 7
f(x) = 3x + 0. Find the inverse f⁻¹(x).
- Write y = 3x + 0 and swap x and y.
- Rearrange for y: y = (x − 0) / 3.
- Answer: f⁻¹(x) = (x − 0) / 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.
Every free resource for Composite Functions in Context
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Frequently asked
- Is this Grade 3 Composite Functions in Context 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 Working with Composite Functions, Introducing Composite Functions, Domain and Range. 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 Composite Functions in Context?
- Move on to Function Notation, Domain and Range, Inverse Functions, which build directly on this idea.
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