1. Functions and Their Properties Functions are correspondences between two sets of numbers. For example, distance and time, or the radius of a circle and its area. A function consists of a domain and rule.

2. Functions and Their Properties Functions are correspondences between two sets of numbers. For example, distance and time, or the radius of a circle and its area. A function consists of a domain and rule. Domain – a set of real numbers

3. Functions and Their Properties Functions are correspondences between two sets of numbers. For example, distance and time, or the radius of a circle and its area. A function consists of a domain and rule. Domain – a set of real numbers Rule – assigns each umber in the domain one and only one number ( called the range )

4. Functions and Their Properties Functions also begin using notation a little bit different than our normal equation format. It uses script letters f, g, and h to define the function and its rule.

5. Functions and Their Properties Functions also begin using notation a little bit different than our normal equation format. It uses script letters f, g, and h to define the function and its rule. The function acts like a machine that inputs a domain value, and a range value is produced.

6. Functions and Their Properties Functions also begin using notation a little bit different than our normal equation format. It uses script letters f, g, and h to define the function and its rule. The function acts like a machine that inputs a domain value, and a range value is produced. NOTATION : “f” is the name of the function “x” is the variable that represents the domain values for input Referred to as “ f of x” 2x+6 is the rule of the function

7. Functions and Their Properties When something other than the defined domain value appears inside the parentheses, we substitute that item into the function wherever the domain value appears.

8. Functions and Their Properties When something other than the defined domain value appears inside the parentheses, we substitute that item into the function wherever the domain value appears. EXAMPLE :

9. Functions and Their Properties When something other than the defined domain value appears inside the parentheses, we substitute that item into the function wherever the domain value appears. EXAMPLE :

10. Functions and Their Properties When something other than the defined domain value appears inside the parentheses, we substitute that item into the function wherever the domain value appears. EXAMPLE :

11. Functions and Their Properties When something other than the defined domain value appears inside the parentheses, we substitute that item into the function wherever the domain value appears. EXAMPLE :

12. Functions and Their Properties When something other than the defined domain value appears inside the parentheses, we substitute that item into the function wherever the domain value appears. EXAMPLE :

13. Functions and Their Properties To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”.

14. Functions and Their Properties To find the domain of a rational function, set the denominator equal to zero to find those values that create the undefined situation. To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”.

15. Functions and Their Properties To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”. To find the domain of a rational function, set the denominator equal to zero to find those values that create the undefined situation. EXAMPLE : Find the domain for

16. Functions and Their Properties To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”. To find the domain of a rational function, set the denominator equal to zero to find those values that create the undefined situation. EXAMPLE : Find the domain for

17. Functions and Their Properties To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”. To find the domain of a rational function, set the denominator equal to zero to find those values that create the undefined situation. EXAMPLE : Find the domain for So when x = 1, the denominator equals zero.

18. Functions and Their Properties To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”. To find the domain of a rational function, set the denominator equal to zero to find those values that create the undefined situation. EXAMPLE : Find the domain for So when x = 1, the denominator equals zero. Therefore, the domain of this function is all real number EXCEPT 1

19. Functions and Their Properties To find the domain of a rational that contains a square root, set the denominator greater than or equal to zero to find where the root will be positive or zero. To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”.

20. Functions and Their Properties To find the domain of a rational that contains a square root, set the denominator greater than or equal to zero to find where the root will be positive or zero. To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”. EXAMPLE : Find the domain for

21. Functions and Their Properties To find the domain of a rational that contains a square root, set the denominator greater than or equal to zero to find where the root will be positive or zero. To define the domain of a function, we have to consider any values that might result in the rule becoming “undefined”. The two most commonly used are division by zero and a negative square root. The domain then becomes all real numbers and excludes those that give an “undefined”. EXAMPLE : Find the domain for Domain