A function is one of the key concepts in many areas of mathematics.

a) Define a function, a 1-1 function, an onto function, an inverse of a function. Provide examples for each as you define them. Use graphs and diagrams to support your ideas. Mathtype to type all mathematical notation is advised.

b) Functions were also studied in various mathematics courses. In these courses, the functions had additional properties. Discuss these functions, including their additional properties, and provide examples. Note: Some of these functions may have different names in different courses. Use graphs and diagrams to support your ideas. Mathtype to type all mathematical notation is advised.

i) Linear Algebra.

ii) Abstract Algebra.

iii) Modern Geometry.

Mathtype to type all mathematical notation is advised.