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Year 11 Algebra Functions

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Year 11 Algebra Functions

Show your working where requested. Give exact answers unless a question asks for rounding.

Function notation and evaluation

1.Let f(x) = 4x − 7. Find f(3), f(−2), and f(0).

2.For g(x) = x² − 3x − 4, calculate g(5).

3.Which relation defines y as a function of x?

{(0, 1), (2, 3), (0, 4), (5, 6)}
{(−1, 2), (0, 2), (1, 3), (2, 4)}
{(3, 1), (3, 2), (4, 3), (5, 4)}
Both the first and third relations

4.For p(x) = 3x + 8, find the input x for which p(x) = 23.

Linear and quadratic functions

5.A linear function passes through (0, 5) and (4, −3). Find its rule in the form f(x) = mx + c.

6.For q(x) = x² − 6x + 5, find the y-intercept, both x-intercepts, and the vertex coordinates.

7.A bike-hire shop charges a fixed fee of $4.80 plus $1.65 for each hour hired. Write a function H(t) for the total cost in dollars after t hours.

8.Using H(t) = 4.80 + 1.65t, calculate the hire cost for 6 hours.

Quadratic functions and applications

9.Compare y = x² and y = 3x². Describe how changing the coefficient of x² from 1 to 3 changes the parabola. Then compare y = x² and y = −x².

10.Compare y = x² with y = x² + 4. Describe the effect of adding 4, and state the new y-intercept.

11.A toy rocket rises from a platform 3 metres above the ground. Its height after t seconds is h(t) = −4t² + 16t + 3. Find its maximum height. Show how you locate the vertex.

12.For the rocket model h(t) = −4t² + 16t + 3, find when it reaches the ground. Give the positive time to 2 decimal places.

13.In h(t) = −4t² + 16t + 3, explain what the coefficient −4 tells you about the rocket's motion.