1. Chapter 8: Linear Functions & Graphing 8.4 Writing Rules for Linear Functions

2. Function Notation we’ve used:y = 2x – 1 now we’re going to use:f(x) = 2x – 1 –read as “f of x is 2x minus 1” f(x) is a notation, does not mean “f times x”!! means f(the equation) as a function of x –plug in an x, and get a value out

3. Function Machine x f(x) or y domain = input range = output

4. Function Rule equation that describes a function usually we find a “change” (slope of line) we also find a value for when the input = 0

5. Example 1 Paulo works at a local store. Each week, he earns a $300 salary plus a 3% commission on his sales. Write a function rule that relates total earnings to sales.

6. Example 1 Paulo works at a local store. Each week, he earns a $300 salary plus a 3% commission on his sales. Find Paulo’s earnings for one week if his sales are $2,500.

7. Example 1a Scrumptious Snack Mix is sold by mail order. It costs $3/lb, plus $4 for shipping and handling. Write a function rule for the total cost c(p) based on the number of pounds p bought. Use your function to find the total cost of 5 lb of snack mix.

8. Using a table… given a table of values find a pattern –ex. twice x plus 3 –ex. half of x minus 4 remember your slope formula!

9. Example 2 Write a rule for the linear function in the table below. Xf(x) -2-5 01 27 413

10. Example 2a Write a rule for the linear function in the table below. Xf(x) -2 00 12 24

11. Example 2a Write a rule for the linear function in the table below. Xf(x) -36 00 3-6 6-12

12. Example 2a Write a rule for the linear function in the table below. Xf(x) -6-11 -4-7 -2-3 01

13. Example 3 Write a rule for the linear function graphed: (0,-1) (4,1)

14. Example 3a Write a rule for the function graphed: (-2,4) (1,1)

15. Homework