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

Question

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

niks18 · Answer

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

stne · Answer

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 ?

niks18 · Answer

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) graph.jpg

JeffTargetTestPrep · Answer

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

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=b7JoMX0gk8M

samarpan.g28 · Answer

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.

bumpbot · Answer

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