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Piecewise Functions: Absolute Value & Cost Representation

Learn how to write absolute value functions and piecewise functions. Calculate costs and wages using piecewise functions.

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Piecewise Functions: Absolute Value & Cost Representation

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  1. Piecewise Functions Write the equation of the absolute value function as a piecewise function: How many parts? 2 1st part when x is… less than zero. 2nd part when x is… greater than or equal to zero.

  2. Piecewise Functions Write the equation of the absolute value function as a piecewise function: How many parts? 2 1st part when x is… less than zero. 2nd part when x is… greater than or equal to zero. Equation of the part less than zero: y = -2x

  3. Piecewise Functions Write the equation of the absolute value function as a piecewise function: How many parts? 2 1st part when x is… less than zero. 2nd part when x is… greater than or equal to zero. Equation of the part greater than or equal to zero: y = 2x

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  6. Piecewise Functions State the domain and range of the piecewise function: Domain: All real numbers Range: y ≥ 0

  7. Piecewise Functions Write the equation of the piecewise function: How many parts? 2 1st part when x is… less than 5. 2nd part when x is… greater than or equal to 5. Equation of the part less than 5: y = -x + 5 Equation of the part greater than or equal to 5: y = x – 5

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  9. Piecewise Functions The postal service charges $1 for a package up to 4 ounces and $0.50 for each additional ounce up to 13 ounces. Write a piecewise function to represent the cost C  in dollars for weight x in ounces? Function for ≤ 4 oz: C = 1 Function for > 4: C = 1 + 0.5(x – 4)

  10. Piecewise Functions You have a summer job that pays time and a half for overtime. That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7. a. Write a function that gives your weekly pay P in terms of the number of hours h you work. b. How much will you get paid if you work 45 hours? For up to 40 hours: 7h

  11. Piecewise Functions You have a summer job that pays time and a half for overtime. That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7. a. Write a function that gives your weekly pay P in terms of the number of hours h you work. b. How much will you get paid if you work 45 hours? For over 40 hours: 280 + 1.5(7)(h – 40) 10.5h – 140

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  13. Piecewise Functions For 45 hours the pay will be $332.50.

  14. Piecewise Functions Jacob was paid an hourly wage of $8 for 30 hours per week and 1.5 times the hourly wage for more than 30 hours. Write a function represent Jacob’s wages. Function for ≤ 30 hours: y = 8x Function for > 30 hours: y = 240 + 1.5(8)(x – 30) y = 12x – 120

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