Piecewise Applications (and Spiral Review)

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!

Match the graph with the correct equation.

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Tags

CCSS.HSF-IF.C.7B

Which of the following graphs is the graph of  $f\left(x\right)=$  

 $2x-3,\ \ \ x\le3$  
 $-3x+10,\ \ \ x>3$  

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• 

Tags

CCSS.HSF-IF.C.7B

The amount Leah 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

BingeFlix is a new streaming service where you pay $3 for each tv show you watch in a month up to the 20th show. Every show after that is only $1. Which piecewise function below matches the scenario?

•  $f\left(x\right)=\left\{3x\ \ \ \ \ ,\ 0<x\le20\right\}$    
   $\left\{x\ +60\ \ \ \ ,\ x>20\right\}$  
  

•  $f\left(x\right)=\left\{3x\ \ \ \ \ ,\ 0<x\le20\right\}$   
   $\left\{x\ \ \ \ \ ,\ \ x>20\right\}$  
  

•  $f\left(x\right)=\left\{3x\ \ \ \ \ ,\ 0<x\le20\right\}$  
   $\left\{x+40\ \ \ \ \ ,\ x>20\right\}$  

•  $f\left(x\right)=\left\{3x\ \ \ \ \ ,\ 0<x\le20\right\}$  
   $\left\{2x-60\ \ \ \ \ ,\ \ x>20\right\}$  

Willy Wonka has opened a new candy shop in Cary. You can buy 1 pound of candy for $3 per pound, or up to 50 pounds of candy for $2 a pound. If you buy more than 50 pounds of candy, it's $1 per pound plus a $45 dental insurance fee. Which of the below functions best describes the candy prices?

•  $f\left(x\right)=\left\{3x\ \ \ \ \ ,\ 0<x\le1\right\}$    
   $\left\{2x\ \ \ \ ,\ 1<x\le50\right\}$  

   $\left\{x+45\ \ \ \ ,\ x>50\right\}$  
  

•  $f\left(x\right)=\left\{3x\ \ \ \ \ ,\ 0<x\le1\right\}$    
   $\left\{2x\ \ \ \ \ ,\ \ 1<x<50\right\}$ 
    $\left\{x+45,\ \ \ x\ge50\right\}$  
  

•  $f\left(x\right)=\left\{3x\ \ \ \ \ ,\ 0<x\le1\right\}$ 
   $\left\{2\left(x-1\right)+3,\ \ 1<x\le50\right\}$  
   $\left\{\left(x-50\right)+45\ ,\ 50>x\right\}$  

Which of the following equations could have this graph?

• y=-(x+1)(x-2)(x-4)

• y=(x+1)²(x-3)(x-1)³

• y = 3x³ – 2x + 1

• y=(x+1)³(x-3)(x-1)²

Tags

CCSS.HSA.APR.B.3

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

• TRUE
• FALSE

Find the roots of

y = -x² - 5x + 12

• -4.9 and -0.1

• -8.54 and 8.54

• -0.45 and 3.55

• -6.77 and 1.77

Tags

CCSS.HSA-REI.B.4B