Study Notes
Non-linear functions include various types of graphs that are not straight lines, such as curves. These functions can be represented by different equations, including quadratic, cubic, reciprocal, and exponential functions.
- Quadratic Graph — a graph represented by a quadratic equation, typically forming a parabola. Example: y = x^2 - 4x + 3
- Trigonometric Graph — a graph representing trigonometric functions like sine, cosine, etc. Example: y = sin x
- Cubic Graph — a graph represented by a cubic equation, which can have an S-shaped curve. Example: y = x^3 + 2x^2 - 4
- Reciprocal Graph — a graph of the form y = 1/x, which has a hyperbolic shape. Example: y = 1/x
- Exponential Function — a function of the form f(x) = a^x, where 'a' is a constant base greater than 0. Example: f(x) = 2^x
Exam Tips
Key Definitions to Remember
- A quadratic graph is a parabola.
- An exponential function is of the form f(x) = a^x.
- A trigonometric function has a domain of angles and a range of [-1, 1].
Common Confusions
- Confusing the shapes of quadratic and cubic graphs.
- 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 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 the domain and range of functions
- Knowledge of how to find gradients using tangents