Question

How do you graph $y=\left| x-2 \right|$ ?

Answer 1

First we will draw the graph of $y=x$ . if we know the graph of $f\left( x \right)$ we can draw the graph of $f\left( \left| x \right| \right)$ call it $g\left( x \right)$ then we can draw $g\left( x-2 \right)$ which is $f\left( \left| x-2 \right| \right)$ by shifting the graph 2 units towards right.

Complete step by step answer:
To draw the graph of $y=\left| x-2 \right|$ lets draw the graph of $y=x$. The graph of $y=x$ is straight line passing through origin with slope 1.

If we $y=f\left( x \right)$ then $f\left( \left| x \right| \right)$ will be $y=\left| x \right|$ . The graph of $f\left( \left| x \right| \right)$ is same as $y=f\left( x \right)$ when x is greater than 0 and the graph of $f\left( \left| x \right| \right)$ is symmetric about Y axis. Basically $f\left( \left| x \right| \right)$ is $f\left( x \right)$ when x is greater than 0 and $f\left( -x \right)$ when x is less than 0.
So let’s draw the graph of $y=\left| x \right|$

Let take $g\left( x \right)$ as $\left| x \right|$ then $g\left( x-2 \right)$ will be $\left| x-2 \right|$ . We know that if to draw graph of $g\left( x-2 \right)$ we need to shift the graph of $g\left( x \right)$ 2 units toward right.
So if we shift the graph of $\left| x \right|$ 2 units towards right we will get the graph of $\left| x-2 \right|$
So let’s do that

The above graph is the graph of $y=\left| x-2 \right|$ .

Note: We draw the graph by write the definition of $y=\left| x-2 \right|$ .
$\left| x-2 \right|$ = $x-2$ when x is greater equal to than 2
= $2-x$ when x is less than equal to 2
we can draw graph of $x-2$ when x is greater than or equal to 2

We can draw the graph of $2-x$ when x is less than or equal to 2

Merging 2 graphs