1. Some Revision on Concepts …questions from students in these few days

2. Domains, co-domain and range

3. Functions: Domain, Co-domain and Range Consider the function: What is its domain? Co-domain? And Range? Answer: Basically you don’t know! ◦ Since you need to know what values to be put into x.

4. Functions: Domain, Co-domain and Range Recall Function: x={0,1,2,3}y={0,1,4,9} x={-2,-1,0}y={4,1,0} DomainCo-domain function Range DomainRange

5. Functions: Domain, Co-domain and Range Domain: The set of all possible values of x to be put into the function. Range: The set of all values of y under the function. Co-domain: The set of all possible values of y, not necessarily only those calculated values. Domain Co-domain function Range 1,2,3,4 1,2,3,4,5,6,7,8,9,10, 11,12,13,14,15,16, … 1,4,9, 16

6. Functions: Domain, Co-domain and Range The curious question: ◦ Given the domain and range, who cares about the co-domain? Co-domain: The set of values of y obtained before actual calculating the function. For example: domain={-1, 2, -3, 4} co-domain={all positive integers} range={1,4,9,16} 1,2,3,4 1,2,3,4,5,6,7,8,9,10, 11,12,13,14,15,16, … 1,4,9, 16

7. Some examples Any problems with each examples? DomainCo-domainRangeOK? {1,2,3,4}{1,4,9,16} OK {1,2,3,4}{All real numbers} {1,4,9,16}OK {1,2,3,4}{All positive integers} {1,4,9,16,17}Not OK {1,2,3,4}{1,4,9}{1,4,9,16}Not OK {-1,0,1,2,3}{All positive integers} ???What should the range be?

8. Graphs of exponential and logarithmic functions and their transformations

9. Two basic graphs that you need to remember by heart The normal exponential ◦ Example: The normal logarithmic ◦ Example:

10. The normal reflections

12. The reciprocal relations Explanation: Equivalent to a reflection in x axis. Explanation: Equivalent to a reflection in x axis.

13. The reciprocal relations Explanation: Equivalent to a reflection in y axis. Explanation: Equivalent to a reflection in y axis.

14. Exponential Function: A short summary Logarithmic Function:

15. The inverse relations Explanation: Exponential and logarithmic relation is basically a switch in the role of x and y. Explanation: Exponential and logarithmic relation is basically a switch in the role of x and y. Also means

16. The inverse relations