📊 Part 1: Function Types and Features

1. Match each function type with its general form:

1. Linear Function

2. Quadratic Function

3. Exponential Function

A. y = a · b^x

B. y = mx + c

C. y = ax² + bx + c

2. Circle the correct answer: What does the gradient 'm' represent in a linear function y = mx + c?

The y-intercept

The rate of change (slope)

The x-intercept

The domain

3. For the quadratic function y = -2x² + 8x - 6, identify the key features:

a) The coefficient 'a' is _______ which means the parabola opens _________

b) The axis of symmetry is at x = _______

c) The vertex coordinates are ( _____ , _____ )

📈 Part 2: Graphing Functions

4. Sketch the graph of y = 2x + 3 on the grid below. Label the y-intercept and show the gradient.

5. For the exponential function y = 3 × (0.5)^x, tick all statements that are correct:

This represents exponential growth

This represents exponential decay

The y-intercept is 3

As x increases, y approaches 0

The base is greater than 1

6. Complete the table of values for y = x² - 4x + 3:

🔄 Part 3: Function Transformations

7. Describe how each transformation affects the parent function y = x²:

a) y = x² + 5: _________________________________

b) y = (x - 3)²: _________________________________

c) y = -x²: _________________________________

d) y = 2x²: _________________________________

8. Circle the correct transformation: The function y = 2^(x+1) - 3 is transformed from y = 2^x by:

1 unit right, 3 units up

1 unit left, 3 units down

1 unit up, 3 units left

1 unit down, 3 units right

9. Sketch the transformation y = (x - 2)² + 1 compared to the parent function y = x²:

🌍 Part 4: Real-World Applications

10. A ball is thrown upward and its height (in metres) is modelled by h(t) = -5t² + 20t + 2, where t is time in seconds.

a) What is the initial height of the ball? _______ metres

b) At what time does the ball reach its maximum height? _______ seconds

c) What is the maximum height reached? _______ metres

11. A population of bacteria doubles every hour. If there are initially 100 bacteria, write the exponential function that models this growth:

12. Explain the difference between exponential growth and exponential decay, giving one real-world example of each:

🎯 Part 5: Problem Solving

13. The cost of a mobile phone plan is $30 per month plus $0.50 per gigabyte of data used.

a) Write a linear function C(g) for the total monthly cost based on gigabytes used: ________________

b) What would be the cost for using 15 gigabytes? $______

c) If someone's bill was $42, how many gigabytes did they use? ______ GB

14. Compare and contrast the key features of these three functions:

Function A: y = 3x - 2

Function B: y = x² - 4x + 3

Function C: y = 2 × 3^x

15. Challenge: Describe what happens to the graph of y = 2^x when it undergoes the transformation y = -2^(x-1) + 4:

Functions and Transformations

Functions and Transformations

📊 Part 1: Function Types and Features

📈 Part 2: Graphing Functions

🔄 Part 3: Function Transformations

🌍 Part 4: Real-World Applications

🎯 Part 5: Problem Solving

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