Function; an Entity Relating Variables and Parameters

This chapter introduces the concept of function as a bivariate relation and general techniques for analyzing it. It provides ways of transitioning between various function representations and pinpoints parallelism between methods of their analyses. Functions are built of variables and parameters that affect the functions’ shape and locations in the XY coordinates. Therefore, attention is given to differentiating between these entities. Structures of formulas as seen through the prism of functions and their roles in mathematics and natural sciences will also be discussed. An emphasis will be given to transitioning from formulas to bivariate functions. Such links enrich students’ mathematical reasoning to quantify natural phenomena and advance their scientific knowledge. This chapter also introduces the function average and instantaneous rates of change in the contexts of monotonicity and concavity. Presented detailed solutions to stated problems within the topics are signify the universality of mathematics operations and encourage learners’ investigations.