How Do You Create a Sketch From Information Given or a Real-World Context?

Create a sketch by translating every piece of given information into a graphical feature, then joining those features with the correct overall shape. In IB Mathematics: Applications and Interpretation, a sketch must show key features clearly, but it does not need to be perfectly accurate or drawn to scale.

This is part of SL 2.3, Graph of a function, studied by both SL and HL students.

A Reliable Method

1. Define the axes. Identify the independent variable for the horizontal axis and the dependent variable for the vertical axis. Include contextual labels and units, such as time in hours and temperature in degrees Celsius.
2. Determine the domain. Use the context to decide the meaningful input values. For example, time since an experiment began may require $t \geq 0$.
3. Plot key features. Mark given intercepts, endpoints, maxima, minima, vertices, intersections, or asymptotes.
4. Identify the model’s shape. Decide whether the information suggests a linear, quadratic, exponential, cubic, or sinusoidal relationship.
5. Join the features appropriately. Use a smooth curve unless the relationship is discrete or piecewise linear.
6. Check the context. Remove graph sections that are mathematically possible but contextually meaningless.