Graphs of Functions

Summary and Exam Tips for Graphs of Functions

Graphs of Functions is a subtopic of Functions, which falls under the subject Mathematics in the Cambridge IGCSE curriculum. This section focuses on understanding and sketching various types of function graphs, such as parabolas, hyperbolas, cubic graphs, reciprocal graphs, and trigonometric graphs.

• Parabolas are the graphs of quadratic functions, characterized by their u-shaped or n-shaped curves, depending on the sign of the leading coefficient.
• Cubic graphs represent cubic functions and typically have two turning points: a minimum and a maximum.
• Reciprocal graphs are hyperbolas, often represented by equations like $y = \frac{1}{x}$.
• Absolute value functions have graphs with sharp turns, reflecting their non-negative nature.
• Trigonometric graphs such as sine, cosine, and tangent have distinct periodic properties. The sine and cosine graphs repeat every 360º, while the tangent graph repeats every 180º and includes vertical asymptotes.
• Asymptotes are lines that a graph approaches but never touches, crucial for understanding the behavior of functions as they extend towards infinity.

Exam Tips

• Understand Graph Shapes: Familiarize yourself with the shapes of different function graphs. Recognizing whether a graph is a parabola, hyperbola, or cubic can help you quickly identify the function type.
• Use Tables of Values: Constructing tables of values is a reliable method to plot accurate graphs, especially for quadratic and cubic functions.
• Identify Key Features: Pay attention to turning points, asymptotes, and periodicity in trigonometric graphs. These features are often tested in exams.
• Practice Sketching: Regularly practice sketching graphs from equations and vice versa. This will enhance your ability to visualize and interpret functions.
• Review Past Papers: Solving past paper questions can provide insights into common exam patterns and help you manage time effectively during the test.