Question

Which of the following is the graph of $y=|x-2|$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

we know that the graph of $y=|x|$

Let $f\left(x\right)=|x|$ and $f^{\prime }\left(x\right)=|x-2|$

$f\left(x\right)=0,$when $x=0$

$f^{\prime }\left(x\right)=0,$when $x=2$

It means ,if we are travelling in the +ve x direction from negative side,we will see the graph of $f^{\prime }\left(x\right)$ as a

delayed version of f(x).

If there is $y_1=|x_1|$,then f'(x) will attain this value after 2 more units.

i.e.,$y_1=f^{\prime }(x_1+2)=|x_1+2-2|=|x_1|$.

so the graph of |x| shifted to the right by 2 units will give graph of $|x-2|$.so the option b is correct.