Maths Extension 1 Year 11 - Module 1 - Lesson 1
Introduction to Extension 1 Functions
Name
Date
Class
1. Lesson focus
Function notation, domain and range. A function assigns exactly one output to each allowed input; evaluate by substitution and respect stated domains.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. For g(x)=1/(x−4), state the domain.
3. For h(x)=x² on −2≤x≤1, state its range.
3. Challenge
Find the zeros of p(x)=x²−4x+3.
4. Multiple choice
For f(x)=x², which is its range when the domain is all real numbers?
A. [1,∞)
B. (-∞,∞)
C. (-∞,0]
D. [0,∞)
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. For f(x)=x²−2x+3, find f(−1).
f(−1)=1+2+3=6.
2. For g(x)=1/(x−4), state the domain.
All real x except x=4, where the denominator is zero.
3. For h(x)=x² on −2≤x≤1, state its range.
The minimum is 0 at x=0 and maximum 4 at x=−2; range [0,4].
Challenge. Find the zeros of p(x)=x²−4x+3.
Factor (x−1)(x−3)=0; zeros are x=1 and x=3.
Multiple choice. For f(x)=x², which is its range when the domain is all real numbers?
Correct answer: D. Every square is non-negative, and every y≥0 is attained by x=±√y.
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