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International Baccalaureate Mathematics

Functions

Syllabus Content

The graph of a function; its equation y=f(x). Creating a sketch from information given or a context, including transferring a graph from screen to paper. Using technology to graph functions including their sums and differences

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Official Guidance, clarification and syllabus links:

Students should be aware of the difference between the command terms "draw" and "sketch".

All axes and key features should be labelled.

This may include functions not specifically mentioned in topic 2.

The graph of a function is a fundamental concept in mathematics, representing the relationship between two quantities. The graph is typically drawn in a coordinate system where the independent variable \( x \) is plotted along the horizontal axis and the dependent variable \( y \) along the vertical axis. The equation of a graph is given as \( y = f(x) \), where \( f(x) \) is a function that provides the value of \( y \) for each value of \( x \).

Sketching a graph involves creating a visual representation of the function based on given information or a specific context. This may include transferring a graph from a digital display to paper. It's important to differentiate between 'drawing' and 'sketching' a graph. While drawing requires precision and often involves plotting specific points, sketching is about representing the general shape and key features of the graph.

When sketching graphs, certain key features should be identified and labelled. These include:

Technology plays a crucial role in graphing functions. It allows for the exploration of the behaviour of functions, including their sums and differences. Graphing calculators or software can provide a visual representation, which can then be analysed and sketched. When using technology, it's essential to understand the limitations and ensure that key features of the graph are accurately represented in the sketch.

In summary, graph sketching is a skill that requires understanding the behaviour of functions and their graphical representations. It's not just about creating a visual representation but also about interpreting and understanding the function's characteristics. Remember to label all axes and key features in your sketches to provide a clear and informative graph.

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