Question

help in algebra 2

Answer 1

If g(x) is a transformation of f(x)=|x| that shrinks the graph by a factor of 1/2 and moves it 8 units down, what is g(x) in relation to f(x)?

Answer 2

Rules of \(\large\color{black}{ \rm shifts }\) from \(\large\color{black}{ \rm f(x) }\) to \(\large\color{black}{ \rm g(x) }\).


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


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


\(\large\color{black}{ \rm f(x)=a\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=a\left| x \right| \color{blue}{ +~\rm{c} }}\)
\(\large\color{blue}{ ~\rm {c} }\) units \(\normalsize\color{blue}{ \rm up }\).


\(\large\color{black}{ \rm f(x)=a\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=a\left| x \right| \color{blue}{ -~\rm{c} }}\)
\(\large\color{blue}{ ~\rm{c} }\) units \(\normalsize\color{blue}{ \rm down }\).



Also,
the ` reflection across the X -axis. `

\(\large\color{red}{ \rm f(x)=\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=\color{blue}{ - }\left| x \right| }\)
(the \(\large\color{red}{ ~\rm{f(x)} }\) and \(\normalsize\color{red}{ \rm g(x) }\) are mirrors of each other over the \(\large\color{red}{ \rm{x-axis} }\). ) \(\LARGE\color{white}{ \rm │ }\)



And lastly,
\(\normalsize\color{black}{ \rm{ s~t~r~e~t~c~h~i~n~g} }\)

\(\large\color{black}{ \rm f(x)=\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=\color{blue}{ c }\left| x \right| }\)

For any real number \(\normalsize\color{blue}{ \rm{c} }\), (provided that \(\normalsize\color{blue}{ \rm{c\neq1~~or~~0} }\) )

\(\normalsize\color{black}{ \rm{1)} }\) When \(\normalsize\color{blue}{ \rm{\left| c \right| >1} }\) the (new function) \(\normalsize\color{black}{ \rm{g(x)} }\) is streched \(\normalsize\color{blue}{ \rm{ vertically} }\).
(if comparing to the initial function \(\normalsize\color{black}{ \rm{f(x)} }\). )

\(\normalsize\color{black}{ \rm{2)} }\) When \(\normalsize\color{blue}{ \rm{\left| c \right| <1} }\) the (new function) \(\normalsize\color{black}{ \rm{g(x)} }\) is streched \(\normalsize\color{blue}{ \rm{ horizontally} }\).
(if comparing to the initial function \(\normalsize\color{black}{ \rm{f(x)} }\). )

Answer 3

took me a bit long, sorry.

Answer 4

wow... impressive. :)

Answer 5

it's just latex, although does look neat

Answer 6

not that, the impressive thing is the passion on helping others.

Answer 7

oh ok thank you for the explanation, so then would it be g(x)=1/2|x-8| ?

Answer 8

-8 should be outside the absolute value, for a shift 8 units down

Answer 9

see where I posted the "\(\large\color{blue}{ c }\) units down" ?

Answer 10

so then it'll be g(x)=|1/2x|-8 ?

Answer 11

but the 1/2 is really outside the absolute value, although that doesn't make a difference

Answer 12

like this: \(\large\color{black}{ g(x)= \color{red}{\frac{\LARGE1}{\LARGE 2}}|x|\color{blue}{-8} }\)

Answer 13

do you need to answer the question, `what is g(x) in relation to f(x)?`

Answer 14

ooooh ok i get it :o :o

Answer 15

yw \(\huge\color{black}{_{...} }\)

Answer 16

btw, if you have any thing to ask about latex (I mean literally, almost anything) message me

Answer 17

thank you so much! i appreciate it

Answer 18

\(\large\color{black}{ \rm ~_{\Huge\color{red}{\ddot \smile }}{\large }}\)