Order Matters: Challenge & Extension
Mathematics
Grade 8
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the importance of order in composite functions, including procedural practice, reasoning, real-world applications, and extension challenges.
Worksheet Preview
Full preview • 10 questions
Order Matters: Challenge & Extension
Subject: MathematicsGrade: Grade 8
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Given f(x) = 2x + 3 and g(x) = x^2, compute (f ◦ g)(2).
[2 marks]2.
Calculate (g ◦ f)(4) where f(x) = x - 1 and g(x) = 3x.
[2 marks]3.
If f(x) = x/2 and g(x) = x + 5, find (f ◦ g)(10).
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step questions with full explanations.
1.
Given functions f(x) = 3x + 2 and g(x) = x^2, explain why (f ◦ g)(x) ≠ (g ◦ f)(x) in general. Illustrate with a specific value of x.
[3 marks]2.
A function h(x) = x + 4, and p(x) = 2x - 1. Find (p ◦ h)(x) and (h ◦ p)(x). Which one results in a larger output for x=5? Explain.
[3 marks]C
Real-world Applications
Apply your understanding of order in functions to real scenarios.
1.
A company applies a markup function f(price) = 1.2 * price, then adds tax g(price) = price + 5. If the original price is $50, find the final price when applying f then g, and compare it to applying g then f. Which order results in a higher final price?
[3 marks]D
Challenge & Extension
Attempt these advanced problems involving order in functions.
1.
Given f(x) = x^2 + 1 and g(x) = 3x - 4, find (f ◦ g)(x) and (g ◦ f)(x). For which values of x are these equal? Show your calculations.
[4 marks]2.
Construct a composite function h(x) = (g ◦ f)(x) where f(x) = x + 2 and g(x) = x^3. What is h(4)? Explain the significance of order here.
[3 marks]E
Mixed Review
Answer these varied questions to review your understanding of order matters.
1.
Identify the mistake: If f(x)=2x and g(x)=x+3, a student claims (f ◦ g)(x)=2x+3. Is this correct? Explain.
[2 marks]2.
Order of composition affects the output. Given f(x)=x^2 and g(x)=2x, find (f ◦ g)(x) and (g ◦ f)(x) at x=3. Which is larger?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet