Question 1

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.   P(6,−2) ,Q(−6,6) P ( 6 , - 2 )  , Q ( - 6,6 ) P(6,−2) ,Q(−6,6)

Accepted Answer

A)  y =  −23- \frac { 2 } { 3 }−32​  x-2 
B)  y =  −32- \frac { 3 } { 2 }−23​  x-6 
C)  y =  −23- \frac { 2 } { 3 }−32​  x+2 
D)  y =  −23- \frac { 2 } { 3 }−32​  x-4 
E)  y =  −23- \frac { 2 } { 3 }−32​  x+6

Question 2

Find the center and radius of the circle, and sketch its graph. 
  (x−12) 2+(y−12) 2=494\left( x - \frac { 1 } { 2 } \right)  ^ { 2 } + \left( y - \frac { 1 } { 2 } \right)  ^ { 2 } = \frac { 49 } { 4 }(x−21​) 2+(y−21​) 2=449​

Accepted Answer

A)  Centre  (12,12) \left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right) (21​,21​)   , Radius  494\frac { 49 } { 4 }449​    
B)  Centre  (12,12) \left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right) (21​,21​)   , Radius  494\frac { 49 } { 4 }449​    
C)  Centre  (12,12) \left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right) (21​,21​)   , Radius  72\frac { 7 } { 2 }27​   
D)  Centre  (−12,−12) \left( - \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right) (−21​,−21​)   , Radius  74\frac { 7 } { 4 }47​   
E)  Centre  (12,12) \left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right) (21​,21​)   , Radius  72\frac { 7 } { 2 }27​

Question 3

Let M denote the midpoint of the line segment joining (4, 3)  and (11, 6) .Find the distance from M to the point (-6, -5) .Round the answer to the nearest tenth. ​

Accepted Answer

A)  16.7
B)  16.1
C)  16.5
D)  15.9
E)  16.2

Question 4

Does the function have an inverse function?

Accepted Answer

A) True 
 B)False

Question 5

Find the inverse function of g(x)  = x2 - 3 informally.

Accepted Answer

A)    g−1(x) =x−32g ^ { - 1 } ( x )  = \sqrt [ 2 ] { x - 3 }g−1(x) =2x−3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    g−1(x) =(x+3) 2g ^ { - 1 } ( x )  = ( x + 3 )  ^ { 2 }g−1(x) =(x+3) 2 
C)    g−1(x) =x2+3g ^ { - 1 } ( x )  = x ^ { 2 } + 3g−1(x) =x2+3 
D)    g−1(x) =x+32g ^ { - 1 } ( x )  = \sqrt [ 2 ] { x + 3 }g−1(x) =2x+3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
E)    g−1(x) =(x−3) 2g ^ { - 1 } ( x )  = ( x - 3 )  ^ { 2 }g−1(x) =(x−3) 2

Question 6

Write the standard form of the equation of the circle with the given characteristics. center: (-1, -5) ; radius: 6

Accepted Answer

A)    (x−1) 2+(y−5) 2=36( x - 1 )  ^ { 2 } + ( y - 5 )  ^ { 2 } = 36(x−1) 2+(y−5) 2=36   
B)    (x+5) 2+(y+1) 2=6( x + 5 )  ^ { 2 } + ( y + 1 )  ^ { 2 } = 6(x+5) 2+(y+1) 2=6 
C)    (x+5) 2+(y+1) 2=36( x + 5 )  ^ { 2 } + ( y + 1 )  ^ { 2 } = 36(x+5) 2+(y+1) 2=36 
D)    (x−5) 2+(y−1) 2=6( x - 5 )  ^ { 2 } + ( y - 1 )  ^ { 2 } = 6(x−5) 2+(y−1) 2=6 
E)    (x+1) 2+(y+5) 2=36( x + 1 )  ^ { 2 } + ( y + 5 )  ^ { 2 } = 36(x+1) 2+(y+5) 2=36

Question 7

Given the points (-6, -8)  and (4, -6) .Find a third point so that the three points form the vertices of a right triangle. ​

Accepted Answer

A)  (-16, 4) 
B)  (-11, 17) 
C)  (-6, -9) 
D)  (5, -6) 
E)  (4, 6)

Question 8

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

Accepted Answer

A)    L=0.3SL = 0.3 SL=0.3S 
B)    L=0.7SL = 0.7 SL=0.7S 
C)    S=0.7LS = 0.7 LS=0.7L 
D)    S=70LS = 70 LS=70L 
E)    S=0.3LS = 0.3 LS=0.3L

Question 9

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Accepted Answer

A)  Horizontal shift of  y=x3;y=(x−4) 3y = x ^ { 3 } ; y = ( x - 4 )  ^ { 3 }y=x3;y=(x−4) 3 
B)  Vertical shift of  y=x2;y=(x−4) 2y = x ^ { 2 } ; y = ( x - 4 )  ^ { 2 }y=x2;y=(x−4) 2 
C)  Vertical shift of  y=x2;y=(x+4) 2y = x ^ { 2 } ; y = ( x + 4 )  ^ { 2 }y=x2;y=(x+4) 2 
D)  Horizontal shift of  y=x2;y=(x+4) 2y = x ^ { 2 } ; y = ( x + 4 )  ^ { 2 }y=x2;y=(x+4) 2 
E)  Vertical shift of  y=x3;y=(x+4) 3y = x ^ { 3 } ; y = ( x + 4 )  ^ { 3 }y=x3;y=(x+4) 3

Question 10

Approximate the coordinates of the points.

Accepted Answer

A)    A:(6,−12) ,B:(34,3) ,C:(−2,5) ,D:(43,−43) A : \left( 6 , - \frac { 1 } { 2 } \right)  , B : \left( \frac { 3 } { 4 } , 3 \right)  , C : ( - 2,5 )  , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right) A:(6,−21​) ,B:(43​,3) ,C:(−2,5) ,D:(34​,−34​)  
B)    A:(6,−12) ,B:(34,−1) ,C:(−2,5) ,D:(43,−43) A : \left( 6 , - \frac { 1 } { 2 } \right)  , B : \left( \frac { 3 } { 4 } , - 1 \right)  , C : ( - 2,5 )  , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right) A:(6,−21​) ,B:(43​,−1) ,C:(−2,5) ,D:(34​,−34​)  
C)    A:(6,−12) ,B:(34,0) ,C:(−2,5) ,D:(43,−43) A : \left( 6 , - \frac { 1 } { 2 } \right)  , B : \left( \frac { 3 } { 4 } , 0 \right)  , C : ( - 2,5 )  , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right) A:(6,−21​) ,B:(43​,0) ,C:(−2,5) ,D:(34​,−34​)  
D)    A:(6,−12) ,B:(34,1) ,C:(−2,5) ,D:(43,−43) A : \left( 6 , - \frac { 1 } { 2 } \right)  , B : \left( \frac { 3 } { 4 } , 1 \right)  , C : ( - 2,5 )  , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right) A:(6,−21​) ,B:(43​,1) ,C:(−2,5) ,D:(34​,−34​)  
E)    A:(6,−12) ,B:(34,2) ,C:(−2,5) ,D:(43,−43) A : \left( 6 , - \frac { 1 } { 2 } \right)  , B : \left( \frac { 3 } { 4 } , 2 \right)  , C : ( - 2,5 )  , D : \left( \frac { 4 } { 3 } , - \frac { 4 } { 3 } \right) A:(6,−21​) ,B:(43​,2) ,C:(−2,5) ,D:(34​,−34​)

Question 11

Select the correct graph, showing f and g are inverse functions.   f(x) =6x+1,g(x) =x−16f ( x )  = 6 x + 1 , g ( x )  = \frac { x - 1 } { 6 }f(x) =6x+1,g(x) =6x−1​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

The number of people playing tennis T (in millions)  in the United States from 2000 through 2007 can be approximated by the function 
  T(t) =0.0235t4−0.3401t3+2.556t2−6.86t+23.8T ( t )  = 0.0235 t ^ { 4 } - 0.3401 t ^ { 3 } + 2.556 t ^ { 2 } - 6.86 t + 23.8T(t) =0.0235t4−0.3401t3+2.556t2−6.86t+23.8   
And the U.S.population P (in millions)  from 2000 through 2007 can be approximated by the function  P(t) =5.8t+224.5P ( t )  = 5.8 t + 224.5P(t) =5.8t+224.5  , where t represents the year, with t = 0 corresponding to 2000.
Evaluate the function  h(t) =0.0235t4−0.3401t3+2.556t2−6.86t+23.85.8t+224.5h ( t )  = \frac { 0.0235 t ^ { 4 } - 0.3401 t ^ { 3 } + 2.556 t ^ { 2 } - 6.86 t + 23.8 } { 5.8 t + 224.5 }h(t) =5.8t+224.50.0235t4−0.3401t3+2.556t2−6.86t+23.8​  for t = 0 and 3.

Accepted Answer

A)  h(0)  = 0.1060, h(3)  = 0.0783
B)  h(0)  = 0.3060, h(3)  = 0.2783
C)  h(0)  = -0.2060, h(3)  = -0.1783
D)  h(0)  = 0.1783, h(3)  = 0.2060
E)  h(0)  = -0.1060, h(3)  = -0.0783

Question 13

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Accepted Answer

A)  Vertical stretch of  y=x2,y=2x2y = x ^ { 2 } , y = 2 x ^ { 2 }y=x2,y=2x2 
B)  Horizontal stretch of  y=x3;y=2x3y = x ^ { 3 } ; y = 2 x ^ { 3 }y=x3;y=2x3 
C)  Vertical stretch of  y=x3;y=2x3y = x ^ { 3 } ; y = 2 x ^ { 3 }y=x3;y=2x3 
D)  Vertical stretch of  y=x3;y=−2x3y = x ^ { 3 } ; y = - 2 x ^ { 3 }y=x3;y=−2x3 
E)  Horizontal stretch of  y=x3;y=−2x3y = x ^ { 3 } ; y = - 2 x ^ { 3 }y=x3;y=−2x3

Question 14

Find the distance between the points. ​
(-9, 4) , (3, -5) 
​

Accepted Answer

A)  4
B)  15
C)  9
D)  3
E)  225

Question 15

Find ( fg ) (x) .  f(x) =3xg(x) =5x+7f ( x )  = \sqrt { 3 x } \quad g ( x )  = \sqrt { 5 x + 7 }f(x) =3x​g(x) =5x+7​

Accepted Answer

A)    (fg) (x) =8x+7( f g )  ( x )  = \sqrt { 8 x + 7 }(fg) (x) =8x+7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    (fg) (x) =15x2+7( f g )  ( x )  = \sqrt { 15 x ^ { 2 } + 7 }(fg) (x) =15x2+7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    (fg) (x) =15x2+21x( f g )  ( x )  = \sqrt { 15 x ^ { 2 } + 21 x }(fg) (x) =15x2+21xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    (fg) (x) =x15+21x( f g )  ( x )  = x \sqrt { 15 } + \sqrt { 21 x }(fg) (x) =x15c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+21xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
E)    (fg) (x) =x15+21x( f g )  ( x )  = x \sqrt { 15 + 21 x }(fg) (x) =x15+21xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​

Question 16

Find the x- and y-intercepts of the graph of the equation  y2=8x+5y ^ { 2 } = 8 x + 5y2=8x+5  .

Accepted Answer

A)   x-intercept:  (58,0) \left( \frac { 5 } { 8 } , 0 \right) (85​,0)   y-intercept:  (0,−5) ( 0 , - \sqrt { 5 } ) (0,−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
B)   x-intercept:  (58,0) \left( \frac { 5 } { 8 } , 0 \right) (85​,0)   y-intercept:  (0,±5) ( 0 , \pm \sqrt { 5 } ) (0,±5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
C)   x-intercept:  (0,58) \left( 0 , \frac { 5 } { 8 } \right) (0,85​)   y-intercept:  (0,±5) ( 0 , \pm \sqrt { 5 } ) (0,±5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
D)   x-intercept:  (58,0) \left( \frac { 5 } { 8 } , 0 \right) (85​,0)   y-intercept:  (0,5) ( 0 , \sqrt { 5 } ) (0,5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
E)   x-intercept:  (58,0) \left( \frac { 5 } { 8 } , 0 \right) (85​,0)   y-intercept:  (0,5) ( 0 , \sqrt { 5 } ) (0,5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  .

Question 17

Find a mathematical model representing the statement.(Determine the constant of proportionality.)   
Y varies inversely as x.  (y=9 when x=45.) ( y = 9 	ext { when } x = 45 . ) (y=9 when x=45.)

Accepted Answer

A)    y=9xy = \frac { 9 } { x }y=x9​ 
B)    y=405xy = \frac { 405 } { x }y=x405​ 
C)    y=x405y = \frac { x } { 405 }y=405x​ 
D)    y=45xy = \frac { 45 } { x }y=x45​ 
E)    y=405xy = 405 xy=405x

Question 18

Evaluate the indicated function for  f(x) =x2+6f ( x )  = x ^ { 2 } + 6f(x) =x2+6  and  g(x) =x−5g ( x )  = x - 5g(x) =x−5  .    (f/g) (−4) −g(6) ( f / g )  ( - 4 )  - g ( 6 ) (f/g) (−4) −g(6)

Accepted Answer

A)    −526- \frac { 5 } { 26 }−265​ 
B)    −319- \frac { 31 } { 9 }−931​ 
C)    −913- \frac { 9 } { 13 }−139​ 
D)    −139- \frac { 13 } { 9 }−913​ 
E)    −931- \frac { 9 } { 31 }−319​

Question 19

The monthly cost C of running the machinery in a factory for t hours is given by    C(t) =40t+400C ( t )  = 40 t + 400C(t) =40t+400  The number of hours t needed to produce x products is given by  t(x) =6xt ( x )  = 6 xt(x) =6x  .
Find the equation representing the cost C of manufacturing x products.

Accepted Answer

A)    C(x) =46x+440C ( x )  = 46 x + 440C(x) =46x+440 
B)    C(x) =240x+16,000C ( x )  = 240 x + 16,000C(x) =240x+16,000 
C)    C(x) =40x+406C ( x )  = 40 x + 406C(x) =40x+406 
D)    C(x) =46x+400C ( x )  = 46 x + 400C(x) =46x+400 
E)    C(x) =240x+400C ( x )  = 240 x + 400C(x) =240x+400

Question 20

Find  f∘gf \circ gf∘g  and the domain of the composite function. 
  f(x) =∣x∣,g(x) =x+3f ( x )  = | x | , g ( x )  = x + 3f(x) =∣x∣,g(x) =x+3

Accepted Answer

A)    ∣(x−3) 3∣\left| ( x - 3 )  ^ { 3 } \right|c10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z'/>​(x−3) 3c10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z'/>​  Domain of  f∘gf \circ gf∘g  : all real numbers x
B)    (x+3) 3\sqrt { ( x + 3 )  ^ { 3 } }(x+3) 3c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​  Domain of  f∘gf \circ gf∘g  : all real numbers x
C)    ∣x+3∣| x + 3 |∣x+3∣  Domain of  f∘gf \circ gf∘g  : all real numbers x
D)    ∣(x+3) 3∣\left| ( x + 3 )  ^ { 3 } \right|c10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z'/>​(x+3) 3c10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z'/>​  Domain of  f∘gf \circ gf∘g  : all real numbers x
E)    ∣x−3∣| x - 3 |∣x−3∣  Domain of  f∘gf \circ gf∘g  : all real numbers x

Exam 1: Functions and Their Graphs

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Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ . $( f / g ) ( - 4 ) - g ( 6 )$

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Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$

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Find the distance between the points. (-9, 4) , (3, -5)

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Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line. $P ( 6 , - 2 ) , Q ( - 6,6 )$

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Find ( fg ) (x) . $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

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The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.

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Find the inverse function of g(x) = x² - 3 informally.

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Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y varies inversely as x. $( y = 9 \text { when } x = 45 . )$

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Let M denote the midpoint of the line segment joining (4, 3) and (11, 6) .Find the distance from M to the point (-6, -5) .Round the answer to the nearest tenth.

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Does the function have an inverse function?

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Given the points (-6, -8) and (4, -6) .Find a third point so that the three points form the vertices of a right triangle.

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Find the center and radius of the circle, and sketch its graph. $\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }$

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A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

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Find $f \circ g$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 3$

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Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = 8 x + 5$ .

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Write the standard form of the equation of the circle with the given characteristics. center: (-1, -5) ; radius: 6

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Exam 1: Functions and Their Graphs

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

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Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

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Evaluate the indicated function for f(x) =x2+6f ( x ) = x ^ { 2 } + 6f(x) =x2+6 and g(x) =x−5g ( x ) = x - 5g(x) =x−5 . (f/g) (−4) −g(6) ( f / g ) ( - 4 ) - g ( 6 ) (f/g) (−4) −g(6)

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Select the correct graph, showing f and g are inverse functions. f(x) =6x+1,g(x) =x−16f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }f(x) =6x+1,g(x) =6x−1​

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Find the distance between the points. ​ (-9, 4) , (3, -5) ​

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Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line. P(6,−2) ,Q(−6,6) P ( 6 , - 2 ) , Q ( - 6,6 ) P(6,−2) ,Q(−6,6)

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Find ( fg ) (x) . f(x) =3xg(x) =5x+7f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }f(x) =3x​g(x) =5x+7​

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The monthly cost C of running the machinery in a factory for t hours is given by C(t) =40t+400C ( t ) = 40 t + 400C(t) =40t+400 The number of hours t needed to produce x products is given by t(x) =6xt ( x ) = 6 xt(x) =6x . Find the equation representing the cost C of manufacturing x products.

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Find the inverse function of g(x) = x2 - 3 informally.

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Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y varies inversely as x. (y=9 when x=45.) ( y = 9 \text { when } x = 45 . ) (y=9 when x=45.)

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Let M denote the midpoint of the line segment joining (4, 3) and (11, 6) .Find the distance from M to the point (-6, -5) .Round the answer to the nearest tenth. ​

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Does the function have an inverse function?

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Given the points (-6, -8) and (4, -6) .Find a third point so that the three points form the vertices of a right triangle. ​

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Find the center and radius of the circle, and sketch its graph. (x−12) 2+(y−12) 2=494\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }(x−21​) 2+(y−21​) 2=449​

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Approximate the coordinates of the points.

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A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L.

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Find f∘gf \circ gf∘g and the domain of the composite function. f(x) =∣x∣,g(x) =x+3f ( x ) = | x | , g ( x ) = x + 3f(x) =∣x∣,g(x) =x+3

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Find the x- and y-intercepts of the graph of the equation y2=8x+5y ^ { 2 } = 8 x + 5y2=8x+5 .

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Write the standard form of the equation of the circle with the given characteristics. center: (-1, -5) ; radius: 6

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Correct Answer
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Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ . $( f / g ) ( - 4 ) - g ( 6 )$

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Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$

Correct Answer
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Find the distance between the points. (-9, 4) , (3, -5)

Correct Answer
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Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line. $P ( 6 , - 2 ) , Q ( - 6,6 )$

Correct Answer
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Correct Answer
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Find ( fg ) (x) . $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

Correct Answer
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The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.

Correct Answer
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Find the inverse function of g(x) = x² - 3 informally.

Correct Answer
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Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y varies inversely as x. $( y = 9 \text { when } x = 45 . )$

Correct Answer
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Let M denote the midpoint of the line segment joining (4, 3) and (11, 6) .Find the distance from M to the point (-6, -5) .Round the answer to the nearest tenth.

Correct Answer
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Correct Answer
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Given the points (-6, -8) and (4, -6) .Find a third point so that the three points form the vertices of a right triangle.

Correct Answer
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Find the center and radius of the circle, and sketch its graph. $\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }$

Correct Answer
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Correct Answer
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Find $f \circ g$ and the domain of the composite function. $f ( x ) = | x | , g ( x ) = x + 3$

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Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = 8 x + 5$ .

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