How can students demonstrate their understanding of functions?

Students can effectively demonstrate their understanding of functions by graphing them and interpreting their slope and intercepts. Graphing allows students to visualize the relationship between variables, which is fundamental in understanding how functions operate. By analyzing the slope, students can interpret the rate of change and understand how changes in one variable affect another. The intercepts provide information about where the function crosses the axes, which is critical for understanding the function's overall behavior and key points.

Memorizing function names alone does not convey a deep understanding of how those functions behave in terms of inputs and outputs. Exclusive use of calculators might help in calculating values, but it does not foster a conceptual understanding of function properties or their graphical representations. Avoiding graphing neglects an essential aspect of functions, as visualization plays a crucial role in comprehending their characteristics and applications.