Module A Piecewise Functions and Absolute Value

John has a summer job that pays time and a half for overtime. That is, if John works more than 40 hours per week, his hourly wage for the extra hours is 1.5 times his normal hourly wage of $7.

Evaluate choose the correct explanation for p(50)

• John was able to make $350 as a result of working 50 hours in a single week.

• John was able to make $385 as a result of working 50 hours in a single week.

• John worked 50 hours and as a result earned 10 hours of overtime. His overall income was $360.Which was a $35 increase due to overtime pay.

• John was paid $50 for 350 hours of work.

Tags

CCSS.HSF.IF.A.2

John has a summer job that pays time and a half for overtime. That is, if John works more than 40 hours per week, his hourly wage for the extra hours is 1.5 times his normal hourly wage of $7.

Evaluate choose the correct explanation for p(40)

• John was able to make $280 as a result of working 40 hours in a single week. I found this value by using the first equation in the piecewise function.

• John was able to make $280 as a result of working 40 hours in a single week.I found this value by using the second equation in the piecewise function.

• John worked 40 hours and as a result earned 0 hours of overtime. His overall income was $260.

• John was paid $40 for 280 hours of work.

Tags

CCSS.HSF.IF.A.2

John has a summer job that pays time and a half for overtime. That is, if John works more than 40 hours per week, his hourly wage for the extra hours is 1.5 times his normal hourly wage of $7.

John worked 5 weeks in a row. Two of the weeks john worked 35 hours and 3 of the weeks john worked 47 hours. What statement is true?

• 2p(35) + 3p(47) = $1,477

• 2p(35) + 3p(47) = $1,442

• 35p(2) + 47p(3) = $1,550

• 2p(35) + 3p(47) = $1,551

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

Evaluate the piecewise function given  $h\left(-4\right)$  

• h(-4) = 4 

• h(-4) = -4

• h(-4) = -2

• h(-4)= -4/3

Tags

CCSS.HSF.IF.A.2

Evaluate the piecewise function given 3h(1) - 4h(9)

• -34

• -33

• -15

• 9

Tags

CCSS.HSF.IF.A.2

Solve the following Absolute function  $g\left(x\right)=\ 3\left|2x-4\right|,\ such\ that\ g\left(x\right)=\ 36$  

• (-4 ) U (8)

• [204]

• [2,0]

• [-4] U [8]

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve the following absolute value function  $h\left(x\right)\ =\ \left|x-5\right|,\ such\ that\ h\left(x\right)\ =\ -8$  

• [-3] U [8]

• Undefined/ so solution

• [5]

• (-3) U (8)

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Convert the folowing absolute value functions to a piecewise function $g\left(x\right)\ =\ 2\left|x+3\right|-1$  

•  $2\left(-x-3\right)+1\ \ \ \ \ x<-3$  
    $2\left(x+3\right)\ +1\ \ \ \ \ x\ge-3$  

•  $-2x-7\ \ \ \ \ \ \ \ \ \ \ x<-3$  
   $2x+5\ \ \ \ \ \ \ \ \ \ \ \ x>-3$  
  

•  $-2x-7\ \ \ \ \ \ \ x\le-3$  
   $2x+5\ \ \ \ \ \ \ \ x>-3$  
  

Tags

CCSS.HSF-IF.C.7D

Given the following absolute value function indicate the transformations that occur.
 $j\left(x\right)=\ 2\left|x-3\right|-7$  

• Refection about the x-axis, horizontal translation right 3, vertical translation down 7, vertical stretch of 2

• Horizontal stretch of 2, Horizontal translation of right 3, Vertical Translation of down 7 

• Horizontal translation right 7,  Vertical translation of down 3, vertical stretch of 2.

• Horizontal translation right 3,  Vertical translation of down 7, vertical stretch of 2.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

Given the following absolute value function indicate the transformations that occur.

P(x) = -|1/2x+14| -4

• Reflection about the x-axis, Horizontal translation of left 28, vertical translation of down 4, horizontal stretch of 2.

• Reflection about the x-axis, Horizontal translation of left 14, vertical translation of down 4, horizontal stretch of 2.

• Reflection about the x-axis, Horizontal translation of left 28, vertical translation of down 4, horizontal compression of 2.

• Reflection about the x-axis, Horizontal translation of left 14, vertical translation of down 4, horizontal stretch of 1/2.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2