Question

The graph of y=|x| is reflected in the x-axis and then moved 1 unit to the left and 3 units up. Write an equation of the new function.

Answer 1

okay, here are some rules,

SHIFTS from \(\large\color{black}{ f(x) }\) to form \(\large\color{black}{ g(x) }\).


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~g(x)=\left| x \color{blue}{ -~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm{c} }\) units to the right.


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~g(x)=\left| x \color{blue}{ +~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm{c} }\) units to the left.


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~g(x)=\left| x \right| \color{blue}{ +~\rm{c} }}\)
\(\large\color{blue}{ ~\rm{c} }\) units to up.


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~g(x)=\left| x \right| \color{blue}{ -~\rm{c} }}\)
\(\large\color{blue}{ ~\rm{c} }\) units to down.

Answer 2

when you reflect over the x axis u are ultimately making your y negative

Answer 3

the reflection across x-axis,

\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~g(x)=\color{blue}{ ~\rm{-} }\left| x \right| }\)

Answer 4

So you get it?

Answer 5

Yes thank you!!

Answer 6

can you write or draw your new equation (just in case, you don't have to) ?

Answer 7

\[y=-\left| x+1 \right|+3\]

Answer 8

YES !!

Answer 9

thank you!!

Answer 10

beautiful, and with latex,
\(\huge\color{ blue }{\huge {\bbox[5pt, cyan ,border:2px solid purple ]{ \large\color{black}{ y=\color{red}{ ~\rm{- }} \left| x \color{blue}{ ~\rm{+~1} }\right|\color{green}{ ~\rm{+~3} }} }}}\)

Answer 11

like this,

\(\huge\color{ blue }{\huge {\bbox[5pt, lightcyan ,border:2px solid red ]{ \large\color{black}{ y=\color{red}{ ~\rm{- }} \left| x \color{blue}{ ~\rm{+~1} }\right|\color{green}{ ~\rm{+~3} }} }}}\)

Answer 12

Anyways..... good luck with your math:) You welcome!

Answer 13

Like the boxes!