Question

Write an equation for each translation of y = |x|
left 6 units

Answer 1

$\large\underline{\bold{Solution-}}$

Since, we have to shift 6 units left, so its equation be

$\bf \: y \: = \: |x + 6|$

Additional Information :-

$\sf \: Let y = \: |x|$

Then translation of

$\sf \: of \: h \: units \: up \: means \: y = |x| + h$

$\sf \: of \: h \: units \: down \: means \: y = |x| - h$

$\sf \: of \: h \: units \: right \: means \: y = |x - h|$

$\sf \: of \: h \: units \: left \: means \: y = |x + h|$

Definition of Modulus Function :-

$\begin{gathered}\begin{gathered}\bf \: |x| = \begin{cases} &\sf{ - x \: \: \: when \: x < 0} \\ &\sf{x \: \: \: when \: x \geqslant 0} \end{cases}\end{gathered}\end{gathered}$

$\bf \: Domain \: of \: |x| : \: all \: real \: numbers$

$\bf \: Range \: of \: |x| \: = [0, \infty )$