Functions, domain and range, graphs, zeroes, operations on functions, etc.

1. Functions
Definition, domain, range, graph, polynomial, rational,
radical function, conditional function, zeroes of function

2. Function
Cartesian Product

3. Function
Cartesian Product

4. Function
Cross Product

5. Function
Cross Product

6. Function
Cartesian Product

7. Function
Cartesian Product

8. Function
Cartesian Product

9. Function
Domain and Range, Graph
Functions generate graphs
But not all graphs are functions

10. Function
Graph, Vertical Line Test

11. Function
Graph, Vertical Line Test

12. Function
Polynomial Function
Polynomial functions are defined for all
real numbers
𝐷𝑓 = 𝑅

13. Function
Polynomial functions examples

14. Function
Examples

15. Function
Polynomial functions, examples

16. Function
Rational Function

17. Function
Rational function, graph, domain

18. Function
Rational function

19. Function
Rational Function

20. Function
Radical function
A radical function g is a function in the form
𝑔 𝑥 =
𝑛
𝑓 𝑥
𝐼𝑓 𝑛 = 2𝑘, 𝑘 ∈ 𝑁, 𝐷𝑔 = 𝑥|𝑓(𝑥) ≥ 0
𝑖𝑓 𝑛 = 2𝑘 + 1, 𝑘 ∈ 𝑁, 𝐷𝑔 = 𝑅

21. Function
Radical function

22. Function
Zeroes of function (Roots)

23. Function
Zeroes of function, roots

24. Functions
Zeroes of functions

25. Functions
Zeroes of functions
It has exactly n roots in the set of complex numbers.

26. Function
Factor Theorem

27. Function
Factor Theorem

28. Function
Factor Theorem

29. Function
Conditional function
Conditional function is also referred to as piece-wise function

30. Function
Conditional function/piece-wise function

31. Function
Conditional function/piece-wise function