1. Direct and Inverse Variation

2. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other does as well.

3. How do you know if you have a direct variation? Y varies directly to x Y is directly proportional to x Y = kx for some constant k

4. Inverse Variation An inverse variation function is defined by the equation xy = k.

5. Functions A relationship in which every value of x has a unique value of y. In other words: one y for every x One output for each input One response for each influence One effect for each cause

6. Height is a Function of Weight f(weight) = height Similar to f(x) = mx + b, where f(x) is the function notation to represent y. The letter or part in the parenthesis is always the independent variable. Weight is input (x) and Height is output (y)

7. Example Gross pay is a function of the hours you work times your rate of pay. Your hourly rate of pay is $6.50 a hour. Write the function to represent this situation. Answer is f(h) = 6.50h

8. Domain All the possible values for the independent variable. Range All the possible values for the dependent variable.

9. Make a table to represent some values for your gross pay from the previous example f(h) = 6.50h What are the domain and range of the function listed in the table? What are the practical domain and range? (Assume 40 hour week) hf(h) 213.00 532.50 1065.00 17110.50 40260.00 ** Remember practical domain is the values of the independent variable that makes sense and the practical range is the values you get after applying the domain to the function. (real life scenarios) Answer: Domain { 0 through 40} Range {0 through 260} Answer: Domain {2, 5, 10, 17, 40} Range {13, 32.5, 65, 110.5, 260}