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# Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the

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Senior Manager
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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the [#permalink]

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03 Feb 2018, 11:03
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95% (hard)

Question Stats:

24% (01:11) correct 76% (01:25) wrong based on 55 sessions

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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the following is true about f(x-2)?

A The graph will move up by 2 units
B The graph will move down by 2 units
C The graph will move right by 2 units
D The graph will move left by 2 units
E Cannot be determined

Source: Crackverbal

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Location: India
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Re: Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the [#permalink]

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03 Feb 2018, 11:19
1
devikeerthansr wrote:
Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the following is true about f(x-2)?

A The graph will move up by 2 units
B The graph will move down by 2 units
C The graph will move right by 2 units
D The graph will move left by 2 units
E Cannot be determined

Source: Crackverbal

$$f(x)=(x+2)^2-(x-2)^2=(x+2+x-2)(x+2-x+2)=8x$$

this implies it is a straight line graph

therefore the graph of $$f(x-2)$$ will move $$2$$ units to the right of $$f(x)$$

Option C
Senior Manager
Joined: 27 May 2012
Posts: 484
Re: Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the [#permalink]

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14 Jun 2018, 04:35
niks18 wrote:
devikeerthansr wrote:
Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the following is true about f(x-2)?

A The graph will move up by 2 units
B The graph will move down by 2 units
C The graph will move right by 2 units
D The graph will move left by 2 units
E Cannot be determined

Source: Crackverbal

$$f(x)=(x+2)^2-(x-2)^2=(x+2+x-2)(x+2-x+2)=8x$$

this implies it is a straight line graph

therefore the graph of $$f(x-2)$$ will move $$2$$ units to the right of $$f(x)$$

Option C

Can anybody elaborate on this : if f(x) = 8x the f(x-2) = 8(x-2)
Let y = f(x)
so when y = 8x implies for every value of x, Y is a line parallel to the x - axis . e.g. if x= 1 then the line is y=8 , similarly when x = 2 then the line is y= 16 , these lines are parallel to the x axis and perpendicular to the Y axis so y = 8 means the line has coordinates ( 0 , 8 )
x=3 then y = 24

Basically y = constant is a line parallel to the x axis and perpendicular to the Y axis .
So when y = 8(x-2) , for x= 1 , y = -8
for x= 2, y = 0 ,
For x=3, y = 8
for x= 4 y = 16

So on comparing f(x) = 8x and f(x-2) = 8(x-2)

f(3)= 24 and f(1) = -8
f(4)=32 and f(2) = 0

So it seems the value of f(x) keeps moving up and down rather than left and right , that too not by 2 units !

Can anybody please clarify this ?
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- Stne

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Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82
Re: Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the [#permalink]

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14 Jun 2018, 05:15
1
stne wrote:
niks18 wrote:
devikeerthansr wrote:
Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the following is true about f(x-2)?

A The graph will move up by 2 units
B The graph will move down by 2 units
C The graph will move right by 2 units
D The graph will move left by 2 units
E Cannot be determined

Source: Crackverbal

$$f(x)=(x+2)^2-(x-2)^2=(x+2+x-2)(x+2-x+2)=8x$$

this implies it is a straight line graph

therefore the graph of $$f(x-2)$$ will move $$2$$ units to the right of $$f(x)$$

Option C

Can anybody elaborate on this : if f(x) = 8x the f(x-2) = 8(x-2)
Let y = f(x)
so when y = 8x implies for every value of x, Y is a line parallel to the x - axis . e.g. if x= 1 then the line is y=8 , similarly when x = 2 then the line is y= 16 , these lines are parallel to the x axis and perpendicular to the Y axis so y = 8 means the line has coordinates ( 0 , 8 )
x=3 then y = 24

Basically y = constant is a line parallel to the x axis and perpendicular to the Y axis .
So when y = 8(x-2) , for x= 1 , y = -8
for x= 2, y = 0 ,
For x=3, y = 8
for x= 4 y = 16

So on comparing f(x) = 8x and f(x-2) = 8(x-2)

f(3)= 24 and f(1) = -8
f(4)=32 and f(2) = 0

So it seems the value of f(x) keeps moving up and down rather than left and right , that too not by 2 units !

Can anybody please clarify this ?

hi stne

Kindly refer the attached image for clarity. As you can see each point of the graph f(x) has moved to the right by 2 units forming graph f(x-2)

Attachment:

graph.jpg [ 106.03 KiB | Viewed 143 times ]
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Re: Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the [#permalink]

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17 Jun 2018, 19:35
devikeerthansr wrote:
Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the following is true about f(x-2)?

A The graph will move up by 2 units
B The graph will move down by 2 units
C The graph will move right by 2 units
D The graph will move left by 2 units
E Cannot be determined

As a general function rule, any time we have f(x - k), where k is positive, the graph of the function will move to the right by k units. Thus, the given graph will move to the right by 2 units.

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Re: Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the   [#permalink] 17 Jun 2018, 19:35
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