Summary
Functions and graphs involve understanding different types of equations and their graphical representations.
- Linear Graphs — straight lines with the equation Y = aX + b. Example: Y = 2X + 3 is a linear graph.
- Quadratic Graphs — parabolic curves with equations like Y = ax² + bx + c. Example: Y = x² - 4x + 4 is a quadratic graph.
- Power Functions — graphs with the equation Y = aX^n where n is a constant. Example: Y = X^3 is a power function.
- Exponential Functions — graphs with the equation Y = ka^x where a is a positive integer. Example: Y = 2^x is an exponential function.
Exam Tips
Key Definitions to Remember
- Linear graphs are represented by Y = aX + b.
- Quadratic graphs have the form Y = ax² + bx + c.
- Power functions are expressed as Y = aX^n.
- Exponential functions are written as Y = ka^x.
Common Confusions
- Confusing the shape of quadratic graphs with positive and negative coefficients.
- Misidentifying the line of symmetry in quadratic graphs.
Typical Exam Questions
- What is the gradient of the line Y = 3X + 2? Answer: The gradient is 3.
- Find the x-intercepts of the quadratic equation Y = (x - 2)(x + 1). Answer: x = 2 and x = -1.
- What is the turning point of the quadratic function Y = (x + 2)² - 16? Answer: The turning point is (-2, -16).
What Examiners Usually Test
- Ability to find gradients of linear graphs.
- Identifying maximum and minimum points in quadratic graphs.
- Understanding the behavior of power and exponential functions.