Summary and Exam Tips for Graph of Functions
The Graph of Functions is a subtopic of Sequences, Functions, and Graphs, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. This topic focuses on understanding and interpreting various types of function graphs, including parabolas, hyperbolas, cubic graphs, reciprocal graphs, and trigonometric graphs like sine, cosine, and tangent.
- Parabolas: Construct tables of values to draw and interpret these U-shaped or n-shaped curves, which represent quadratic functions.
- Hyperbolas: Recognize and sketch these two-part curves, which are the graphs of reciprocal functions.
- Cubic Graphs: Identify these graphs by their characteristic two turning points, representing cubic functions with an term.
- Absolute Value Functions: These graphs have sharp turns and are never negative, represented by .
- Trigonometric Graphs:
- Sine and Cosine: These graphs repeat every 360º, with maximum and minimum values of 1 and -1, respectively.
- Tangent: This graph repeats every 180º and features vertical asymptotes at .
- Asymptotes: Lines that a curve approaches but never meets, crucial for understanding the behavior of certain graphs.
Exam Tips
- Understand Graph Shapes: Familiarize yourself with the distinct shapes of parabolas, hyperbolas, and cubic graphs. Recognizing these can help you quickly identify the type of function.
- Use Tables of Values: Practice constructing tables of values for different functions to accurately sketch their graphs.
- Identify Key Features: Pay attention to key features like turning points, asymptotes, and intercepts. These are often tested in exams.
- Practice Sketching: Regularly sketch graphs by hand to reinforce your understanding of their shapes and behaviors.
- Review Past Papers: Solve past paper questions to get a feel for the types of graph-related questions that may appear in exams.
