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1. $f(x) = 1 - |x - 1|$
2. $f(x) =1 + |x - 1|$
3. $f(x) = 2 - |x - 1|$
4. $f(x) = 2 + |x - 1|$

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Please add the text part of the question also "Choose the correct expression for f(x) given in the graph.". I was searching this question based on the text but it was not showing up.
For getting quick answer just use graph transformation techniques (like shifting of origin, adding subtracting constant).

Mentioned graph could be easily obtained via applying transformation on Y = |X| graph.

The equation of line, from coordinates $(1,2)$ to $(3,0)$, where $|x-1|=(x-1)$

$(y-2)=\dfrac{(0-2)}{(3-1)}(x-1)$

$y=2-(x-1)$

$y=2-|x-1|$

The equation of line, from coordinates $(-3,-2)$ to $(1,2)$, where $|x-1|=-(x-1)$

$(y-(-2)) =\dfrac{(2-(-2))}{(1-(-3))}(x-(-3))$

$y=x+1$

$y=2-(-(x-1))$

$y=2-|x-1|$

Note :Equation of line when two coordinates $(x_2,y_2)$ and $(x_1,y_1)$ are given is $(y-y_1)=\dfrac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$

How do we get (y-2)/(x-1) in equation of line?

@sherrin equation of line(given in note) ,  when two points are given.

oh man @Praveen Saini shud have noticed that before, oops!

Here we can cancel options easily !

See that F(0) = 1

A) F(0) => 1 - |x-1| = 1-|-1| = 1-1 = 0 != 1. So A is not answer !

B) F(0) => 1 + |x-1| = 1 + | -1| = 1 + 1 = 2 != 1 So B is not answer !

D) F(0) => 2 + |x-1| = 2 + |-1| = 2 + 1 = 3 != 1 So D is not answer !

Remaining option C is answer !

wow !
Simply Great
How can i see aKash kanase F(0)=1  In this graph. explain .
Here, is another direct method for eliminating the wrong options.

In the above graph, it is clearly shown that f(-1) = 0

a) f(-1) => 1 - |x-1| = 1-|-1-1| = 1-2 = -1.    So (a) is not answer

b) f(-1) => 1 + |x-1| = 1 + | -1-1| = 1+2 = 3 .     So (b) is not answer .

d) f(-1) => 2 + |x-1| = 2 + |-1-1| = 2+2 = 4 .    So (d) is not answer .

(c)  f(-1) => 2 - |x-1| = 2 - |-1-1| = 2-2 = 0  , satisfied the equation.

so,  option (c) is the answer .

I am doing the shift of origin concept and y=mx+C , the mod x graph goes through origin.

then to bring it back to origin. mod x-1

and it is inverted than mod x graph , hence negative of mod x-1

changing Y from 2 to 0 is required to bring it back to origin

hence I think 2 - mod ( x-1 ) is the answer

### 1 comment

I'm not getting this method, can you kindly elaborate?