Module B Outcome 5&6 Inverses

The following points are from the function f(x) = {(1,3),(2,15),(3,8)(4, 2),(5,0)}. What are the points that represent

 $f^{-1}\left(x\right)$  .

•  $f^{-1}\left(x\right)\ =\$  {(0,5), (2,4), (3,1), (8,3), (15,2)}

•  $f^{-1}\left(x\right)=$  {(-1,-3), (-2,-15), (-3,-8),(-4,-2), (-5,0)}

Tags

CCSS.HSF.BF.B.4

The following points are from the function f(x) =f = {(0,5),(2,10),(4,15)(6,20),(5,0)} . What are the points that represent

 $f^{-1}\left(x\right)$  .

•  $f^{-1}\left(x\right)\ =\$  {(0,5), (5,0), (10,2), (15,4), (20,6)}

•  $f^{-1}\left(x\right)=$  {(0,-5), (-2,-10), (-4,-15),(-6,-20), (-5,0)}

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

 $f\left(x\right)=\ \frac{1}{3}x$  

What is true about the following function ? Check all that applies.

•  $f^{-1}\left(x\right)=\ 3x$  

•  $f^{-1}\left(x\right)=\frac{x}{3}$  

• The domain of the linear Function is  $\left(-\infty,\infty\right)$  , the Range of the function is  $\left(-\infty,\infty\right)$ the y- intercept and x intercept is 0.

• The domain of the Exponential Function is  $\left(-\infty,\infty\right)$  , the Range of the function is  $\left(-\infty,\infty\right)$ the y- intercept and x intercept is 0.

•  $f^{-1}\left(9\right)=27$  

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

Check all that apply regarding the linear function  $g\left(x\right)=\frac{-2}{3}x+5$  

• The inverse of g(x) is  $g^{-1}\left(x\right)=-\frac{3x}{2}+\frac{15}{2}$  

• The inverse of g(x) is  $g^{-1}\left(x\right)=-\frac{3}{2}x-\frac{15}{2}$  

•  $g\left(9\right)=-1$  

•  $g^{-1}\left(7\right)=-3$  

Tags

CCSS.HSF.BF.B.4

The average music CD has a diameter of 120mm. A CD player will only play CD's that are within 4mm. Check all of the statments that apply

• The absolute Value inequality

  $\left|d-120\right|\le4$ can be used to calculate the size CD that CD players will play.

• The absolute Value inequality $\left|d-120\right|\ge4$ can be used to calculate the size CD that CD players will play.

• The domain that represents the size of CD's that can be played is [116, 124]

• The domain that represents the size of CD's that can be played is (116, 124)

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Given the function $j\left(x\right)=\left(x-2\right)^2+5\$  with the domain restriction  $x\ge2$  . What is the inverse of j(x)?

•  $j^{-1}\left(x\right)=\sqrt{x-5}+2$  

•  $j^{-1}\left(x\right)=\sqrt{x+5}-2$  

•  $j^{-1}\left(x\right)=-\sqrt{x-5}-2$  

•  $j^{-1}\left(x\right)=-\sqrt{x-5}+2$  

Tags

CCSS.HSF.BF.B.4

Given the quadratic function  $d\left(x\right)=2x^2+12x\ +13$  choose all that apply. 

• If the domain of d(x) is restricted to  $x\ge-3$  the inverse is  $d^{-1}\left(x\right)=\sqrt{\frac{x+5}{2}}-3$  

• If the domain of d(x) is restricted to  $x\le-3$   the inverse is  $d^{-1}\left(x\right)=\ -\sqrt{\frac{\left(x+5\right)}{2}}-3$  

• If the domain of d(x) is restricted to  $x\le-3$  the inverse is  $d^{-1}\left(x\right)=\sqrt{\frac{x+5}{2}}-3$  

• If the domain of d(x) is restricted to  $x\ge-3$   the inverse is  $d^{-1}\left(x\right)=\ -\sqrt{\frac{\left(x+5\right)}{2}}-3$  

Tags

CCSS.HSF.BF.B.4

Given

 $h\left(x\right)=\frac{3}{2}x^3-5$  
Check all that apply

• 
• 
•  $h\left(3\right)=35.5$  

•  $h^{-1}\left(7\right)=2$  
  

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Given the function

 $g\left(x\right)=-2\left|x-5\right|-7$  
check all that apply.

• The range of g(x) is  $\left(-\infty,-7\right]$  

• An increasing interval of function g(x) is  $\left[5,\infty\right)$  

• The piecewise function of g(x)
  
    $2x-17\ \ \ \ x<5$ 
  
     $-2x\ +3\ \ \ \ x\ge5$  

• The piecewise function of g(x)
   $-2x+3\ \ \ \ x\le5$ 
  
   $2x-17\ \ \ \ \ \ x>5$   
  

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

To make a long-distance call, your phone company charges $1.50 to make the connection, and an additional $0.10 for every minute that you are on the line once connected.

Check all that apply

• The function $d\left(m\right)=0.10m\ +1.50$ can be used to model the scenario such that d(m) represents the cost of the long distance call given the amount of time m minutes.

  
  

• The inverse function $d^{-1}\left(m\right)=10m-15$ can be used to model the scenario such that $d^{-1}\left(m\right)$ represents the time in minutes and m represents the cost of the long distance call.

• The inverse function $d^{-1}\left(m\right)=10m-15$ can be used to model the scenario such that $d^{-1}\left(m\right)$ represents the cost of the long distance call given the m minutes.

• $d^{-1}\left(10\right)=85$ indicates that a $10 call last for 85 minutes.

• $d^{-1}\left(10\right)=85$ indicates that a 10 minute call costs $85

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2