1. B ELL -R INGER Express the relation as a table, graph, and mapping diagram. Is the relation a function? {(2, -2), (3, 5), (2, 4), (0, 1)} xy

2. E VALUATING FUNCTIONS

3. FUNCTIONS – I NDEPENDENT AND D EPENDENT AND EVALUATING Learning Target: I will understand the concept of function notation, evaluating functions, as well as dependent and independent variables of a function.

4. W RITING F UNCTIONS Time worked (h) x1233 Amount earned ($) y5101520

5. F UNCTIONS – I NPUT, O UTPUT, I NDEPENDENT, D EPENDENT y = 5x a function with two variables. The input (x) of a function is also the independent variable (x). The output (y) of a function is also the dependent variable (y). The value of the dependent (y) variable depends on, or is a function of, the value of the independent variable (x). For Stacey, the amount she earns is dependent on, or is a function of, the amount of time she works. y = 5x

6. D EPENDENT OR I NDEPENDENT – “I DO ” Identify the independent and dependent variables in each situation. In the winter, more electricity is used when the temperature goes down, and less is used when the temperature rises. Amount of electricity used depends on the temperature Dependent: amount of electricity Independent: temperature

7. D EPENDENT OR I NDEPENDENT – “W E D O ” Identify the independent and dependent variables in each situation. The cost of shipping a package is based on weight. Dependent: cost Independent: weight

8. D EPENDENT OR I NDEPENDENT – “Y OU D O ” Identify the independent and dependent variables in each situation. The faster Ron walks, the quicker he gets home. The time it takes Ron to get home depends on the speed he walks. Dependent: time Independent: speed Paired Worksheet

9. F UNCTION N OTATION Stacey’s baby-sitting gig y = 5x If x is the independent variable and y is dependent variable, then function notation for y is f(x), this reads f of x. So y = f(x) By substitution in Stacey’s function y = 5x f(x) = 5x

10. F UNCTION N OTATION – “I D O ” A lawyers fee is $200 per hour for her services. The fee is dependent on the hours of service. Dependent (y) – fee Independent (x) – hours Let h represent the number of hours worked We can write a function as y = 200h Or f(h) = 200h So if the lawyer works 4 hours, h = 4 f(h) = 200 × h f(4) = 200 × 4 = $800

11. F UNCTION NOTATION – “W E DO ” The admission ticket to Peanut Festival is $7.Each ride also costs $1.50 Write an equation in function notation for cost. Total cost is dependent on number of rides ridden plus $8. Dependent (y) – total cost Independent (x) – number of rides Let r represent the total number of rides y = 1.50r + 7 remember y = f(r) so f(r) = 1.50r + 7 How much would someone spend if they went and rode 10 rides? f(10) = (1.50 × 10) + 7 = $22

12. F UNCTION NOTATION “Y OU D O ” An air conditioning technician charges $75 an hour for his service. Write a equation in function notation to describe his cost. How much would you owe him if he worked for 3.5 hours?

13. J OURNAL W RITE Describe the difference between an independent variable and a dependent variable. Write an equation in function notation for the following situation. An ice-rink charges $3.50 for skates and $1.25 an hour.