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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 03 Feb 2018, 11:03
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

40% (01:30) correct 60% (02:00) wrong based on 179 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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Official Answer
C
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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 03 Feb 2018, 11:19
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devikeerthansr
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
Show more

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

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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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 14 Jun 2018, 04:35
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devikeerthansr
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
Show more

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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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 14 Jun 2018, 05:15
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devikeerthansr
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 ?
Show more

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 5886 times ]
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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 17 Jun 2018, 19:35
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devikeerthansr
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
Show more

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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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 01 Dec 2023, 12:16
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f(x) = (x + 2)^2 - (x - 2)^2, which of the following is true about f(x-2)?

Theory:

1. If f(x) is replaced with f(x-t) (where t is positive), then graph moved to the right by t points
Ex: Let's say f(x) = 2x i.e. y = 2x
=> y = 0 when x = 0
When we replace x with x-2 , i.e. y = f(x-2) = 2(x-2), then
=> y = 0 when x = 2
That means x axis has shifted to the right by 2 points and the origin has moved from (0,0) to (2,0)

2. If f(x) is replaced with f(x+t) (where t is positive), then graph moved to the left by t points
Axis moves from (0,0) to (-t,0)

3. If f(x) is replaced with f(x) + t, then graph moves down by t points
Ex: Let's say f(x) = 2x i.e. y = 2x
=> When y = 0 then x = 0
When we write f(x) + t = 2x i.e. y + t = 2x, then
=> When y = -t then x = 0
Axis moves from (0,0) to (0,-t)

4. If f(x) is replaced with f(x) - t (where t is positive) then graph moves up by t points
Axis moves from (0,0) to (0,t)

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 06 Mar 2024, 22:14
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devikeerthansr
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
Show more
­There is nothing to solve in this question.
From Reflection and Shifting of Graphs, if y=f(x) given where f(x) can be any function (linear, quadrilateral, 3-degree etc) then for f(x-k), the graph will be shifted right by k units. Whereas, for f(x)-k, the graph will be shifted downwards by k units. Option (C) is correct.
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Function f(x) is defined as f(x) = (x + 2)^2 - (x - 2)^2, which of the 26 Apr 2025, 02:32
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