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

− 2 x − 7 x ≤ − 3 -2x-7\ \ \ \ \ \ \ x\le-3 − 2 x − 7 x ≤ − 3 2 x + 5 x > − 3 2x+5\ \ \ \ \ \ \ \ x>-3 2 x + 5 x > − 3

2 ( − x − 3 ) + 1 x < − 3 2\left(-x-3\right)+1\ \ \ \ \ x<-3 2 ( − x − 3 ) + 1 x < − 3 2 ( x + 3 ) + 1 x ≥ − 3 2\left(x+3\right)\ +1\ \ \ \ \ x\ge-3 2 ( x + 3 ) + 1 x ≥ − 3

− 2 x − 7 x < − 3 -2x-7\ \ \ \ \ \ \ \ \ \ \ x<-3 − 2 x − 7 x < − 3 2 x + 5 x > − 3 2x+5\ \ \ \ \ \ \ \ \ \ \ \ x>-3 2 x + 5 x > − 3

Solve the following absolute value h(x)= |x+3|, such that h(x) >10

( − ∞ , − 13 ) U ( 7 , ∞ ) \left(-\infty,-13\right)\ U\ \left(7,\ \infty\right) ( − ∞ , − 1 3 ) U ( 7 , ∞ )

( − ∞ , − 13 ] U [ 7 , ∞ ) \left(-\infty,-13\right]U\ \left[7,\infty\right) ( − ∞ , − 1 3 ] U [ 7 , ∞ )

A carpenter is using a lather to shape the final leg of a hand-crafted table. In order for the leg to fit, it needs to be 150 millimeters wide allowing for a margin of errow of 2.5 millimetes. What is the absolute value in equality that matches the scenario?

∣ x − 150 ∣ ≤ 2.5 \left|x-150\right|\le2.5 ∣ x − 1 5 0 ∣ ≤ 2 . 5

∣ x − 150 ∣ ≥ 2.5 \left|x-150\right|\ge2.5 ∣ x − 1 5 0 ∣ ≥ 2 . 5

∣ x − 2.5 ∣ ≤ 150 \left|x-2.5\right|\le150 ∣ x − 2 . 5 ∣ ≤ 1 5 0

∣ x − 2.5 ∣ ≥ 150 \left|x-2.5\right|\ge150 ∣ x − 2 . 5 ∣ ≥ 1 5 0

Sydney harbor bridge in Australia is 1149 meters long. becaus of the changes in temperature, the bridge can expand and contract by as mush as 420 millimeters (0.42 meters). What is the absolute value inequality that matches the scenario?

∣ x − 1149 ∣ ≤ 0.42 \left|x-1149\right|\le0.42 ∣ x − 1 1 4 9 ∣ ≤ 0 . 4 2

∣ x − 0.42 ∣ ≤ 1149 ∣ ∣ \left|x-0.42\left|\le\ 1149\right|\right| ∣ x − 0 . 4 2 ∣ ≤ 1 1 4 9 ∣ ∣

∣ x − 1149 ∣ ≥ 0.42 \left|x-1149\right|\ge0.42 ∣ x − 1 1 4 9 ∣ ≥ 0 . 4 2

∣ x − 0.42 ∣ ≥ 0.42 \left|x-0.42\right|\ge0.42 ∣ x − 0 . 4 2 ∣ ≥ 0 . 4 2

A carpenter is using a lather to shape the final leg of a hand-crafted table. In order for the leg to fit, it needs to be 150 millimeters wide allowing for a margin of errow of 2.5 millimetes. Within what interval will the leg fit?

( − ∞ , 147.5 ] U [ 152.5 , ∞ ) \left(-\infty,\ 147.5\right]\ U\ \left[152.5,\infty\right) ( − ∞ , 1 4 7 . 5 ] U [ 1 5 2 . 5 , ∞ )

Consider the equation provided. Solve for x ∣ x + 2 ∣ − 3 > 0.5 x + 1 \left|x+2\right|-3\ >0.5x+1 ∣ x + 2 ∣ − 3 > 0 . 5 x + 1

( − ∞ , − 4 ) U ( 4 , ∞ ) \left(-\infty,\ -4\right)U\ \left(4,\ \infty\right) ( − ∞ , − 4 ) U ( 4 , ∞ )

( − ∞ , − 4 ] U [ 4 , ∞ ) \left(-\infty,\ -4\right]\ U\ \left[4,\ \infty\right) ( − ∞ , − 4 ] U [ 4 , ∞ )

( − ∞ , − 3 ) U ( 1 , ∞ ) \left(-\infty,\ -3\right)U\left(1,\ \infty\right) ( − ∞ , − 3 ) U ( 1 , ∞ )

At a dance competition, the duration of each team's routine, m, must be within 1.5 minutes of the required time, 8 minutes. Write an inequality to model the scenario.

∣ t − 8 ∣ ≤ 1.5 \left|t-8\right|\le1.5 ∣ t − 8 ∣ ≤ 1 . 5

∣ t + 1.5 ∣ ≤ 8 \left|t+1.5\right|\le8 ∣ t + 1 . 5 ∣ ≤ 8

∣ t − 8 ∣ ≥ 1.5 \left|t-8\right|\ge1.5 ∣ t − 8 ∣ ≥ 1 . 5

∣ t − 8 ∣ < 1.5 \left|t-8\right|<1.5 ∣ t − 8 ∣ < 1 . 5

Given the absolute value function $$g\left(x\right)=\left|3x-5\right|$$ and the exponential function $$h\left(x\right)=2\left(1.21\right)^x$$ . Check all that apply.

The least solution that satisfies the statement g(x)=h(x) is 0.878

The interval (0.878,2.805) represents the solution set for g(x)<h(x)

The greatest solution that satisfies the statement g(x)=h(x) is 2.805

The interval (0.878, 2.805) represents the solution set for g(x)>h(x)

Module A Piecewise Functions and Absolute Value

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Mathematics

10th - 12th Grade

CCSS covered

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Module A Piecewise Functions and Absolute Value

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

-34

-33

-15

Tags

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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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 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)

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

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

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

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

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

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

Given the following absolute value function indicate the transformations that occur. P(x) = -|1/2x+14| -4

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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 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)

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

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

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

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

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

Given the following absolute value function indicate the transformations that occur.
P(x) = -|1/2x+14| -4