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

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New post 03 Feb 2018, 11:03
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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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Re: Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the  [#permalink]

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New post 03 Feb 2018, 11:19
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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
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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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New post 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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Re: Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the  [#permalink]

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New post 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
graph.jpg [ 106.03 KiB | Viewed 486 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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New post 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.

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