Linear Piecewise Function Word Problems

The amount Lea can earn at her job is shown:

She earns $7 per hour for the first 40 hours.

She earns 1.5 times the hourly wage for every hour over 40 hours.

Which piecewise-defined function best represents Lea’s weekly pay, P(h), where h represents the hours worked?

• P(h)= 7h, 0≤h≤40

  P(h)=10.5h−140, h>40

• P(h)= 7h, 0<h<40

  P(h)= 10.5h−140, h>40

• P(h)= 7h, 0≤h≤40

  P(h)= 10.5h+140, h≥40

• P(h)= 7h, 0<h<40

  P(h)= 10.5h+140, h≥40

Mr. Garrison’s class is collecting aluminum cans to raise money for a trip. The rates are shown:

$0.75 per pound for a collection weighing 10 pounds or less

$1.25 per pound for a collection weighing more than 10 pounds.

What are the domain and range for a collection that weighs more than 10 pounds?

• {x x<10}

  {x x<10}

  
  

  {y y<$12.50}

• {x x>10}

  {x x>10}

  
  

  {y y>$12.50}

• {x x<10}

  {x x<10}

  
  

  {y y<$7.50}

• {x x>10}

  {x x>10}

  
  

  {y y>$7.50}

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

• $1020

• $1140

• $840

• He works for free!

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 45 hour week?

• $2025

• $570

• $680

• He works for free!

• $12.75
• $35
• $43.40
• $27.75

A state income tax uses a piecewise-defined function to calculate taxes owed, T(i), where i is the annual income. What are the taxes owed if Charles has an annual income of $45,000?

• $1,150
• $1,250
• $13,300
• $21,500

A state income tax uses a piecewise-defined function to calculate taxes owed, T(i), where i is the annual income. What are the taxes owed if Charles has an annual income of $30,000?

• $850

• $1,250

• $1,300

• $700

Luke has a $25 gift card to pay for video game rentals. The first five games he can rent for $3 each. After five games each game cost $1. Which piecewise function best represents the balance remaining on the gift card, f(x), after each game rental, x?

• f(x)= 25−3x, 0≤x≤5

  f(x)= 15−x, 6≤x≤10

• f(x)= 25−3x, 0<x<5

  f(x)= 15−x, 6<x<10

• f(x)= 25+3x, 0≤x≤5

  f(x)= 15+x, 6≤x≤10

• f(x)= 25+3x, 0<x<5

  f(x)=15+x, 6<x<10