Question

If $f\left(x\right)=|x|,g\left(x\right)=|x-2|$ and $h\left(x\right)=|x+2|$, then which of the following is/are correct?

• A. If we shift the graph of $f\left(x\right)$ by $2$ units right, we get the graph of $h\left(x\right)$
• B. If we shift the graph of $f\left(x\right)$ by $2$ units right, we get the graph of $g\left(x\right)$
• C. If we shift the graph of $f\left(x\right)$ by $2$ units left, we get the graph of $g\left(x\right)$
• D. If we shift the graph of $f\left(x\right)$ by $2$ units left, we get the graph of $h\left(x\right)$

Answer 1

Answer: (B), (D)

The correct options are
B If we shift the graph of $f\left(x\right)$ by $2$ units right, we get the graph of $g\left(x\right)$
D If we shift the graph of $f\left(x\right)$ by $2$ units left, we get the graph of $h\left(x\right)$

To draw the graph of $f(x+2)$, we shift the graph of $f\left(x\right)$ by $2$ units left.
To draw the graph of $f(x-2)$, we shift the graph of $f\left(x\right)$ by $2$ units right.

As $f\left(x\right)=|x|$, so
$f(x+2)=|x+2|=h\left(x\right)f(x-2)=|x-2|=g\left(x\right)$

Hence, to get the graph of $g\left(x\right),$ we shift the graph of $f\left(x\right)$ by $2$ units right and to get the graph of $h\left(x\right),$ we shift the graph of $f\left(x\right)$ by $2$ units left.