Chapter 8Section 4

Writing Rules for Linear Functions

February 10th, 2009

Writing Rules from Words

Write functions using Function Notation.

f(x) replaces y. That’s all.

Read f(x) as “f of x”.

The Domain Value (x value) is the INPUTINPUT.

The resulting Range Value (y value) is the OUTPUTOUTPUT.

A Function Rule is an equationequation that describes a function.

Function Rule

y = 3x + 7 f(x) = 3x + 7

outputinput

Read it as “f of x is equal to the product of 3 and x, plus 7”.

The Function rule is the Equation that you come up with to compare the Input and the Output.

Real World

Jerry works at a local store. Each week he earns $300 salary plus a 3% commission on his sales.

a) Write a function rule that relates total earnings to sales.

b) Find his earnings for one week if his sales are $2,500.

Function, Part A:Jerry works at a local store. Each week he earns

$300 salary plus a 3% commission on his sales.

A) Write a function rule that relates total earnings to sales.

Total Earnings = $300 + 3% (of Sales)

Total Earnings = y = f(x) = output

$300 = the constant

3% = slope

(of Sales) = x = input

Function, Part B:Jerry works at a local store. Each week he earns

$300 salary plus a 3% commission on his sales.

B) Find his earnings for one week if his sales are $2,500.

t(s) = 300 + 0.03s

t(2,500) = 300 + 0.03s

t(s) = 300 + 0.03(2,500)

t(s) = 300 + 75

t(s) = $375 a week.

S, here, is the input, like f(x). You can make your function notation different from f of x.Here we used t of s.t is dependant on s. So, s can change.

Try This One:

• Scrumptious Snacks 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 lbs of snack mix.

Writing Rules from Tables or Graphs

• To write a function rule from a table, look for a pattern.

• The formula y = mx + b in function notation is, f(x) = mx + b.

• The slope of m is the difference in f(x)-values difference in x-values

• The y-intercept (b) is the value of f(x) when x=0.

Write a rule for the linear function in the table.

• What is the pattern for x and f(x)?

• As the x values increase by 2, the f(x) values increase by 6. So, m = 6/2, or 3.

• When x = 0, f(x) = 1. • So b = 1.• f(x) = 3x + 1 is the rule.

x f(x)

-2 -5

0 1

2 7

4 13

Write the rule for each linear function.

x f(x)

-1 -2

0 0

1 2

2 4

x f(x)

-3 6

0 0

3 -6

6 -12

x f(x)

-6 -11

-4 -7

-2 -3

0 1

f(x) = 2x, because when x =

0, y = 0.

f(x) = -2x, because when x =

0, y = 0.

f(x) = 2x + 1, because when x =

0, y = 1.

Use y=mx+b to Find Rules for Graphs.

• Use the slope-intercept form, f(x)=mx+b, or y=mx+b, when you write a rule for a linear function.

Points (0, -1) and (4, 1)

Find Slope First.

2/4 or ½ = m

Y-Intercepts at?

(0, -1) = b = -1

The rule is f(x) = ½x + -1.

Find the Rule• Write a rule for the function graphed here.

1) Find the Slope, this is m.

2) Find the y-intercept, this is b.

3) Make your function rule.

y = -x + 2

Question?

• What are advantages you see in using a rule for a function rather than listing function values in a table?

Assignment #4: Pages 406-407: 1-20 all.