Question 1

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
- y=−5x2−1y = - 5 x ^ { 2 } - 1y=−5x2−1

Accepted Answer

A)   No symmetry
B)   Origin
C)   x-axis
D)   y-axis E) A) and B)
F) A) and C)

Question 2

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
- y=0.79x2+∣x∣+7y = 0.79 x ^ { 2 } + | x | + 7y=0.79x2+∣x∣+7

Accepted Answer

A)    x -axis
B)    y -axis
C)   No symmetry
D)   Origin E) C) and D)
F) All of the above

Question 3

The graph of the function y  y=f(x)  is given. On the same axes, sketch the graph of f−1(x) y = f ( x )  	ext { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x ) y=f(x)  is given. On the same axes, sketch the graph of f−1(x)   . Use a dashed line for the inverse
function.
-

Accepted Answer

A)  
B)   
C)  
D)   E) B) and C)
F) A) and D)

Question 4

For the pair of functions, perform the indicated operation.
- f(x) =7x2−8x,g(x) =x2−2x−48f ( x )  = 7 x ^ { 2 } - 8 x , g ( x )  = x ^ { 2 } - 2 x - 48 \quadf(x) =7x2−8x,g(x) =x2−2x−48  Find  (fg) (x) \left( \frac { f } { g } \right)  ( x ) (gf​) (x)

Accepted Answer

A)    7x−8−2\frac { 7 x - 8 } { - 2 }−27x−8​ 
B)    7x2−8xx2−2x−48\frac { 7 x ^ { 2 } - 8 x } { x ^ { 2 } - 2 x - 48 }x2−2x−487x2−8x​ 
C)    7−x48\frac { 7 - \mathrm { x } } { 48 }487−x​ 
D)    7xx+1\frac { 7 x } { x + 1 }x+17x​E) A) and B)
F) None of the above

Question 5

Find the inverse of the function.
- f(x) =−5−3xf ( x )  = - 5 - 3 xf(x) =−5−3x

Accepted Answer

A)    f−1(x) =−53+x3\mathrm { f } ^ { - 1 } ( \mathrm { x } )  = - \frac { 5 } { 3 } + \frac { \mathrm { x } } { 3 }f−1(x) =−35​+3x​ 
B)    f−1(x) =53−x3f ^ { - 1 } ( x )  = \frac { 5 } { 3 } - \frac { x } { 3 }f−1(x) =35​−3x​ 
C)    f−1(x) =−53−x3f ^ { - 1 } ( x )  = - \frac { 5 } { 3 } - \frac { x } { 3 }f−1(x) =−35​−3x​ 
D)    f−1(x) =−2−xf ^ { - 1 } ( x )  = - 2 - xf−1(x) =−2−xE) A) and C)
F) A) and B)

Question 6

Determine whether or not the function is one-to-one.
-

Accepted Answer

A)   Yes
B)   NoC) A) and B)
D) undefined

Question 7

The volume of a cylinder whose height is equal to twice its radius is  f(x) =2πx3 cm3\mathrm { f } ( \mathrm { x } )  = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }f(x) =2πx3 cm3  , where  x  is the radius of the cylinder in  cm . Find the inverse of this function.

Accepted Answer

A)    f−1(x) =2πx3f ^ { - 1 } ( x )  = 2 \pi \sqrt [ 3 ] { x }f−1(x) =2π3xc-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)    f−1(x) =12πx3f ^ { - 1 } ( x )  = \frac { 1 } { 2 \pi x ^ { 3 } }f−1(x) =2πx31​ 
C)    f−1(x) =x2π3f ^ { - 1 } ( x )  = \sqrt [ 3 ] { \frac { x } { 2 \pi } }f−1(x) =32πx​c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-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'/>​ 
D)    f−1(x) =x32πf ^ { - 1 } ( x )  = \frac { \sqrt [ 3 ] { x } } { 2 \pi }f−1(x) =2π3xc-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) All of the above
F) B) and C)

Question 8

Find the specified domain and express it in interval notation.
-If  f(x) =3 x+4  and  g(x) =x-x2 , evaluate  (f+g) (3)  .

Accepted Answer

A)   6
B)   19
C)   7
D)    -78 E) A) and B)
F) None of the above

Question 9

Graph the given function as a solid line (or curve)  and its inverse as a dashed line (or curve)  on the same set of axes.
- f(x) =−5xf ( x )  = - 5 xf(x) =−5x

Accepted Answer

A)  
B)  
C)  
D)   E) A) and D)
F) None of the above

Question 10

Aretailer that n games can be sold in a month at a price of 20-0.1n dollars per game. Assume that he buys each game for $13, and sells every one that he buys. if he whishes to make a profit of at least $100 per month on sales of this game, how many games must he sell each month?

Accepted Answer

A)    0≤n≤200 \leq n \leq 200≤n≤20 
B)    20≤n≤5020 \leq n \leq 5020≤n≤50 
C)    20≤n≤7020 \leq n \leq 7020≤n≤70 
D)    25≤n≤3525 \leq n \leq 3525≤n≤35E) None of the above
F) B) and D)

Question 11

Use the quadratic formula or graphing methods to
- 4x2+20x+8≥04 x ^ { 2 } + 20 x + 8 \geq 04x2+20x+8≥0

Accepted Answer

A)    x≥−5+172≈−0.438x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438x≥2−5+17c-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'/>​​≈−0.438 
B)    −5−172≈−4.562≤x≤−5+172≈−0.438\frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562 \leq x \leq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.4382−5−17c-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'/>​​≈−4.562≤x≤2−5+17c-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'/>​​≈−0.438 
C)    x≤−5−172≈−4.562x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562x≤2−5−17c-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'/>​​≈−4.562 
D)    x≤−5−172≈−4.562x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562x≤2−5−17c-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'/>​​≈−4.562  or  x≥−5+172≈−0.438x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438x≥2−5+17c-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'/>​​≈−0.438E) All of the above
F) B) and C)

Question 12

The graph of  y=xy = \sqrt { x }y=x​  is shifted 4 units to the right.

Accepted Answer

A)    y=x−4y = \sqrt { x - 4 }y=x−4c-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)    y=x+4y = \sqrt { x } + 4y=xc-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'/>​+4 
C)    y=x+4y = \sqrt { x + 4 }y=x+4c-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)    y=x−4y = \sqrt { x } - 4y=xc-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'/>​−4E) B) and D)
F) B) and C)

Question 13

Decide whether or not the functions are inverses of each other.
- f(x) =−27x,g(x) =−72xf ( x )  = - \frac { 2 } { 7 } x , \quad g ( x )  = - \frac { 7 } { 2 } xf(x) =−72​x,g(x) =−27​x

Accepted Answer

A)   Yes
B)   No C) A) and B)
D) undefined

Question 14

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary.
- ∣x−8∣≤9| x - 8 | \leq 9∣x−8∣≤9

Accepted Answer

A)    x≤−1x \leq - 1x≤−1  or  x≥17x \geq 17x≥17 
B)    −17≤x≤1- 17 \leq x \leq 1−17≤x≤1 
C)    −1≤x≤17- 1 \leq x \leq 17−1≤x≤17 
D)    −9≤x≤9- 9 \leq x \leq 9−9≤x≤9E) B) and C)
F) None of the above

Question 15

Find the specified domain and express it in interval notation.
-If f(x) =2x+10  and g(x) =x2+3 , evaluate  (gf) (2) \left( \frac { g } { f } \right)   { ( 2 )  }(fg​) (2)  .

Accepted Answer

A)    12\frac { 1 } { 2 }21​ 
B)   2
C)   98
D)   21 E) B) and C)
F) A) and C)

Question 16

Sketch the graph of the pair of functions. Use a dashed line for g(x) 
- f(x) =x2,g(x) =−14(x+3) 2+4f ( x )  = x ^ { 2 } , g ( x )  = - \frac { 1 } { 4 } ( x + 3 )  ^ { 2 } + 4f(x) =x2,g(x) =−41​(x+3) 2+4

Accepted Answer

A)  
B)  
C)  
D)   E) A) and D)
F) None of the above

Question 17

Use the quadratic formula or graphing methods to
- 6x2−27x+6≥06 x ^ { 2 } - 27 x + 6 \geq 06x2−27x+6≥0

Accepted Answer

A)    x≥9+654≈4.266x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266x≥49+65c-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'/>​​≈4.266 
B)    9−654≈0.234≤x≤9+654≈4.266\frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234 \leq x \leq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.26649−65c-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'/>​​≈0.234≤x≤49+65c-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'/>​​≈4.266 
C)    x≤9−654≈0.234x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234x≤49−65c-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'/>​​≈0.234 
D)    x≤9−654≈0.234x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234x≤49−65c-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'/>​​≈0.234  or  x≥9+654≈4.266x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266x≥49+65c-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'/>​​≈4.266E) All of the above
F) A) and B)

Question 18

The graph of the function y  y=f(x)  is given. On the same axes, sketch the graph of f−1(x) y = f ( x )  	ext { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x ) y=f(x)  is given. On the same axes, sketch the graph of f−1(x)   . Use a dashed line for the inverse
function.
-A size 4 dress in Country C is size 42 in Country D. A function that converts dress sizes in Country  CCC  to those in Country  DDD  is  f(x) =x+38f ( x )  = x + 38f(x) =x+38 . Find a formula for the inverse of this function.

Accepted Answer

A)    f−1(x) =x+38f ^ { - 1 } ( x )  = x + 38f−1(x) =x+38 
B)    f−1(x) =x−38f ^ { - 1 } ( x )  = \frac { x } { - 38 }f−1(x) =−38x​ 
C)    f−1(x) =x38\mathrm { f } ^ { - 1 } ( \mathrm { x } )  = \frac { \mathrm { x } } { 38 }f−1(x) =38x​ 
D)    f−1(x) =x−38f ^ { - 1 } ( x )  = x - 38f−1(x) =x−38E) B) and C)
F) A) and B)

Question 19

Solve the equation
- (x+3) 3/2=27( x + 3 )  ^ { 3 / 2 } = 27(x+3) 3/2=27

Accepted Answer

A)    x=14 
B)    x=9 
C)    x=6 
D)    x=12  E) A) and B)
F) A) and C)

Question 20

Sketch the graph of the pair of functions. Use a dashed line for g(x) 
- f(x) =x2,g(x) =15x2f ( x )  = x ^ { 2 } , g ( x )  = \frac { 1 } { 5 } x ^ { 2 }f(x) =x2,g(x) =51​x2

Accepted Answer

A)  
B)   
C)  
D)   E) C) and D)
F) B) and C)

Exam 4: Additional Topics With Functions

Find the inverse of the function. - $f ( x ) = - 5 - 3 x$

Correct Answer
verified

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| x - 8 | \leq 9$

Correct Answer
verified

The volume of a cylinder whose height is equal to twice its radius is $\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }$ , where x is the radius of the cylinder in cm . Find the inverse of this function.

Correct Answer
verified

Decide whether or not the functions are inverses of each other. - $f ( x ) = - \frac { 2 } { 7 } x , \quad g ( x ) = - \frac { 7 } { 2 } x$

Correct Answer
verified

The graph of $y = \sqrt { x }$ is shifted 4 units to the right.

Correct Answer
verified

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 } A) B) C) D)$

Correct Answer
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Correct Answer
verified

Find the specified domain and express it in interval notation. -If f(x) =2x+10 and g(x) =x²+3 , evaluate $\left( \frac { g } { f } \right) { ( 2 ) }$ .

Correct Answer
verified

Correct Answer
verified

Find the specified domain and express it in interval notation. -If f(x) =3 x+4 and g(x) =x-x² , evaluate (f+g) (3) .

Correct Answer
verified

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = - 5 x ^ { 2 } - 1$

Correct Answer
verified

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f ( x ) = - 5 x$

Correct Answer
verified

Use the quadratic formula or graphing methods to - $6 x ^ { 2 } - 27 x + 6 \geq 0$

Correct Answer
verified

Use the quadratic formula or graphing methods to - $4 x ^ { 2 } + 20 x + 8 \geq 0$

Correct Answer
verified

Aretailer that n games can be sold in a month at a price of 20-0.1n dollars per game. Assume that he buys each game for $13, and sells every one that he buys. if he whishes to make a profit of at least $100 per month on sales of this game, how many games must he sell each month?

Correct Answer
verified

Correct Answer
verified

Solve the equation - $( x + 3 ) ^ { 3 / 2 } = 27$

Correct Answer
verified

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = 0.79 x ^ { 2 } + | x | + 7$

Correct Answer
verified

For the pair of functions, perform the indicated operation. - $f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Correct Answer
verified

Determine whether or not the function is one-to-one. -

Correct Answer
verified

Exam 4: Additional Topics With Functions

Find the inverse of the function. - f(x) =−5−3xf ( x ) = - 5 - 3 xf(x) =−5−3x

Correct AnswerverifiedShow Answer

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - ∣x−8∣≤9| x - 8 | \leq 9∣x−8∣≤9

Correct AnswerverifiedShow Answer

The volume of a cylinder whose height is equal to twice its radius is f(x) =2πx3 cm3\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }f(x) =2πx3 cm3 , where x is the radius of the cylinder in cm . Find the inverse of this function.

Correct AnswerverifiedShow Answer

Decide whether or not the functions are inverses of each other. - f(x) =−27x,g(x) =−72xf ( x ) = - \frac { 2 } { 7 } x , \quad g ( x ) = - \frac { 7 } { 2 } xf(x) =−72​x,g(x) =−27​x

Correct AnswerverifiedShow Answer

The graph of y=xy = \sqrt { x }y=x​ is shifted 4 units to the right.

Correct AnswerverifiedShow Answer

Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x) =x2,g(x) =15x2f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }f(x) =x2,g(x) =51​x2

Correct AnswerverifiedShow Answer

The graph of the function y y=f(x) is given. On the same axes, sketch the graph of f−1(x) y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x ) y=f(x) is given. On the same axes, sketch the graph of f−1(x) . Use a dashed line for the inverse function. -

Correct AnswerverifiedShow Answer

Find the specified domain and express it in interval notation. -If f(x) =2x+10 and g(x) =x2+3 , evaluate (gf) (2) \left( \frac { g } { f } \right) { ( 2 ) }(fg​) (2) .

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Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x) =x2,g(x) =−14(x+3) 2+4f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4f(x) =x2,g(x) =−41​(x+3) 2+4

Correct AnswerverifiedShow Answer

Find the specified domain and express it in interval notation. -If f(x) =3 x+4 and g(x) =x-x2 , evaluate (f+g) (3) .

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Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y=−5x2−1y = - 5 x ^ { 2 } - 1y=−5x2−1

Correct AnswerverifiedShow Answer

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - f(x) =−5xf ( x ) = - 5 xf(x) =−5x

Correct AnswerverifiedShow Answer

Use the quadratic formula or graphing methods to - 6x2−27x+6≥06 x ^ { 2 } - 27 x + 6 \geq 06x2−27x+6≥0

Correct AnswerverifiedShow Answer

Use the quadratic formula or graphing methods to - 4x2+20x+8≥04 x ^ { 2 } + 20 x + 8 \geq 04x2+20x+8≥0

Correct AnswerverifiedShow Answer

Aretailer that n games can be sold in a month at a price of 20-0.1n dollars per game. Assume that he buys each game for $13, and sells every one that he buys. if he whishes to make a profit of at least $100 per month on sales of this game, how many games must he sell each month?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the equation - (x+3) 3/2=27( x + 3 ) ^ { 3 / 2 } = 27(x+3) 3/2=27

Correct AnswerverifiedShow Answer

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y=0.79x2+∣x∣+7y = 0.79 x ^ { 2 } + | x | + 7y=0.79x2+∣x∣+7

Correct AnswerverifiedShow Answer

For the pair of functions, perform the indicated operation. - f(x) =7x2−8x,g(x) =x2−2x−48f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quadf(x) =7x2−8x,g(x) =x2−2x−48 Find (fg) (x) \left( \frac { f } { g } \right) ( x ) (gf​) (x)

Correct AnswerverifiedShow Answer

Determine whether or not the function is one-to-one. -

Correct AnswerverifiedShow Answer

Find the inverse of the function. - $f ( x ) = - 5 - 3 x$

Correct Answer
verified

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| x - 8 | \leq 9$

Correct Answer
verified

The volume of a cylinder whose height is equal to twice its radius is $\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }$ , where x is the radius of the cylinder in cm . Find the inverse of this function.

Correct Answer
verified

Decide whether or not the functions are inverses of each other. - $f ( x ) = - \frac { 2 } { 7 } x , \quad g ( x ) = - \frac { 7 } { 2 } x$

Correct Answer
verified

The graph of $y = \sqrt { x }$ is shifted 4 units to the right.

Correct Answer
verified

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 } A) B) C) D)$

Correct Answer
verified

Correct Answer
verified

Find the specified domain and express it in interval notation. -If f(x) =2x+10 and g(x) =x²+3 , evaluate $\left( \frac { g } { f } \right) { ( 2 ) }$ .

Correct Answer
verified

Correct Answer
verified

Find the specified domain and express it in interval notation. -If f(x) =3 x+4 and g(x) =x-x² , evaluate (f+g) (3) .

Correct Answer
verified

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = - 5 x ^ { 2 } - 1$

Correct Answer
verified

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f ( x ) = - 5 x$

Correct Answer
verified

Use the quadratic formula or graphing methods to - $6 x ^ { 2 } - 27 x + 6 \geq 0$

Correct Answer
verified

Use the quadratic formula or graphing methods to - $4 x ^ { 2 } + 20 x + 8 \geq 0$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Solve the equation - $( x + 3 ) ^ { 3 / 2 } = 27$

Correct Answer
verified

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = 0.79 x ^ { 2 } + | x | + 7$

Correct Answer
verified

For the pair of functions, perform the indicated operation. - $f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

Correct Answer
verified

Correct Answer
verified