Write an equation for the following translation of y=-|x| (2 units down)

Question

solomonzelman · Answer

Rules of  $\large\color{black}{ \rm shifts }$  from  $\large\color{black}{ \rm f(x)  }$  to   $\large\color{black}{ \rm g(x)  }$.


$\large\color{black}{ \rm f(x)=-\left|  x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=-\left|  x \color{blue}{  -~\rm{c}   }\right| }$
$\large\color{blue}{  ~\rm {c}   }$ units to the $\normalsize\color{blue}{ \rm right }$.


$\large\color{black}{  \rm f(x)=-\left|  x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=-\left|  x \color{blue}{  +~\rm{c}   }\right| }$
$\large\color{blue}{  ~\rm {c}   }$ units to the $\normalsize\color{blue}{ \rm left }$.


$\large\color{black}{ \rm f(x)=-\left|  x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=-\left|  x  \right| \color{blue}{  +~\rm{c}  }}$
$\large\color{blue}{  ~\rm {c}   }$ units $\normalsize\color{blue}{ \rm up }$.


$\large\color{black}{ \rm f(x)=-\left|  x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=-\left|  x  \right| \color{blue}{  -~\rm{c}  }}$
$\large\color{blue}{  ~\rm{c}   }$ units $\normalsize\color{blue}{ \rm down }$.

solomonzelman · Answer

tell me if you need more help.