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

CCan 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