Piecewise Functions Write the equation of the absolute

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

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

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

Piecewise Functions •

Piecewise Functions •

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

Piecewise Functions Write the equation of the piecewise function: How many parts? 2 1 st part when x is… less than 5. 2 nd 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

• Piecewise Functions

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)

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: 7 h

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. 5 h – 140

• Piecewise Functions

Piecewise Functions For 45 hours the pay will be $332. 50.

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 = 8 x Function for > 30 hours: y = 240 + 1. 5(8)(x – 30) y = 12 x – 120