2. Interpretation of Domain and Range of a function f

3. Domain is the Set of all x where f is well defined Range is the set of all values f( x ) Where x is in the domain f

4. Graphical Approach to Domain and Range Example 1: Find the natural domain and Range of the graph of the function f below The function f represents f (x ) = x 2. f is well defined everywhere in R. Therefore, Domain = R Range Domain Every value of f is non-negative ( greater than or equal to 0. Therefore, Range =

5. More illustrations of Domain and Range of a graph of a function f These two graphs seem similar, but the domain and range are different This graph does not end on both sides Domain = Range = This graph ends, it is also not defined at x = –2 and well defined at x =2 Domain = Range =

6. Class Exercise 1 Find the natural domain and range of the following graphs Domain =Range =Domain = Range =

7. Algebraic Approach to find the Domain of a function f Example 1: Find the natural domain of the following functions Solution: ( 1 ) f is a linear function. f is well-defined for all x. Therefore, Domain = R ( 2 ) f is a square root function. f is well defined when Domain = (3) f is well defined when Domain = (4) f is well defined when and -5 Domain =

8. The End