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8.4 Rules For Linear Functions

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Jessca Lundin
Jessca Lundin

The document discusses writing rules for linear functions from words, tables, and graphs. It provides examples of writing function rules based on descriptions of real-world contexts, tables showing input-output pairs, and graphs of linear functions. Writing a rule involves identifying the slope and y-intercept to write the function in the form f(x)=mx+b. A rule allows easy calculation of output values for any input rather than just listed points.

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Chapter 8 Section 4 Writing Rules for Linear Functions February 10 th , 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 INPUT . The resulting Range Value (y value ) is the OUTPUT . A Function Rule is an equation that describes a function.
Function Rule y = 3 x + 7 f ( x ) = 3 x + 7 output input 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. Write a function rule that relates total earnings to sales. 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. 13 4 7 2 1 0 -5 -2 f ( x ) x
Write the rule for each linear function. 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. 4 2 2 1 0 0 -2 -1 f ( x ) x -12 6 -6 3 0 0 6 -3 f ( x ) x 1 0 -3 -2 -7 -4 -11 -6 f ( x ) x
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. Find the Slope, this is m. Find the y-intercept, this is b. 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.

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8.4 Rules For Linear Functions

  • 1. Chapter 8 Section 4 Writing Rules for Linear Functions February 10 th , 2009
  • 2. 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 INPUT . The resulting Range Value (y value ) is the OUTPUT . A Function Rule is an equation that describes a function.
  • 3. Function Rule y = 3 x + 7 f ( x ) = 3 x + 7 output input 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.
  • 4. Real World Jerry works at a local store. Each week he earns $300 salary plus a 3% commission on his sales. Write a function rule that relates total earnings to sales. Find his earnings for one week if his sales are $2,500.
  • 5. 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
  • 6. 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.
  • 7. 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.
  • 8. 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.
  • 9. 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. 13 4 7 2 1 0 -5 -2 f ( x ) x
  • 10. Write the rule for each linear function. 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. 4 2 2 1 0 0 -2 -1 f ( x ) x -12 6 -6 3 0 0 6 -3 f ( x ) x 1 0 -3 -2 -7 -4 -11 -6 f ( x ) x
  • 11. 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.
  • 12. Find the Rule Write a rule for the function graphed here. Find the Slope, this is m. Find the y-intercept, this is b. Make your function rule. y = -x + 2
  • 13. Question? What are advantages you see in using a rule for a function rather than listing function values in a table?
  • 14. Assignment #4: Pages 406-407: 1-20 all.