Study Notes
Non-linear functions include various types of graphs such as quadratic, cubic, reciprocal, and exponential functions. These functions are represented by curves rather than straight lines.
- Quadratic Graph — a graph represented by a parabola. Example: y = x^2 - 4x + 3
- Trigonometric Graph — a graph that involves trigonometric functions like sine. Example: y = sin x
- Cubic Graph — a graph represented by a cubic equation. Example: y = x^3 + 2x^2 - 4
- Reciprocal Graph — a graph represented by a reciprocal function. Example: y = 1/x
- Exponential Function — a function of the form f(x) = a^x where 'a' is a constant greater than 0. Example: f(x) = 2^x
Exam Tips
Key Definitions to Remember
- A quadratic graph is represented by a parabola.
- An exponential function is of the form f(x) = a^x.
- The domain of an exponential function is all real numbers.
Common Confusions
- Confusing the shape of a quadratic graph with a cubic graph.
- Misunderstanding the domain and range of exponential functions.
Typical Exam Questions
- What is the shape of a quadratic graph? A parabola
- How do you find the gradient of a non-linear graph? By drawing a tangent to the curve and finding its gradient
- What is the domain of an exponential function? All real numbers
What Examiners Usually Test
- Understanding of different types of non-linear graphs
- Ability to identify and describe the domain and range of functions