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

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

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

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

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.

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.

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.

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!

Example 2 Write a rule for the linear function in the table below. Xf(x)

Example 2a Write a rule for the linear function in the table below. Xf(x)

Example 2a Write a rule for the linear function in the table below. Xf(x)

Example 2a Write a rule for the linear function in the table below. Xf(x)

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

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

Homework