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Year 11 Algebra Functions

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Year 11 Algebra Functions worksheet preview

Year 11 Algebra Functions

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📚 Part 1: Function Notation and Evaluation

1. Given f(x) = 3x - 5, find:

a) f(2) = _______

b) f(-1) = _______

c) f(0) = _______

2. If g(x) = x² + 2x - 3, calculate g(4):
3. Which of the following represents a function?

{(1,2), (2,3), (1,4), (3,5)}

{(1,2), (2,3), (3,4), (4,5)}

{(1,2), (2,2), (3,2), (4,2)}

Both B and C

4. For h(x) = 2x + 1, find the value of x when h(x) = 9:

📈 Part 2: Linear and Quadratic Functions

5. A linear function passes through points (0, -2) and (3, 4). Write the function in the form f(x) = mx + c:
6. For the quadratic function f(x) = x² - 4x + 3, identify:

a) y-intercept: _______

b) x-intercepts (factorise to find): _______ and _______

c) Vertex coordinates: (___, ___)

7. A taxi company charges a base fee of $3.50 plus $2.20 per kilometre. Write a function C(d) for the cost in dollars for d kilometres travelled:
8. Using your function from question 7, calculate the cost for a 12-kilometre journey:

🔍 Part 3: Investigation and Problem Solving

9. Investigation Task: Consider the function f(x) = ax² + bx + c where a, b, and c are constants.

a) How does changing the value of 'a' affect the shape of the parabola? Give specific examples:

b) What happens to the graph when 'c' changes? Explain with examples:

10. Real-world Application: A ball is thrown upward from a height of 2 metres. Its height h(t) in metres after t seconds is given by h(t) = -5t² + 10t + 2.

a) What is the maximum height reached by the ball? Show your working:

b) After how many seconds does the ball hit the ground? (Hint: When does h(t) = 0?)

c) Explain what the coefficient -5 represents in this real-world context:

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