Question

HELPPPPPP ANYONE !!!
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x - 16?
It is the graph of y = x translated to the right 16 units.
It is the graph of y = x translated up 16 units.
It is the graph of y = x, where the slope is decreased by 16.
It is the graph of y = x translated to the left 16 units

Answer 1

@SolomonZelman

Answer 2

\(\large\color{ slate }{\large {\bbox[5pt, ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline \texttt{Shifts} ~~~\tt from~~~ {f(x)~~~\tt to~~~g(x)}&~\tt{c~~~units~~~~} \\
\hline
\\f(x)= bx ~~~~\rm{\Rightarrow}~~~~ g(x)= b(x \normalsize\color{red }{ -~\rm{c} }) &~\rm{to~~the~~right~} \\
\text{ } \\f(x)= bx ~~~~\rm{\Rightarrow}~~~~ g(x)= b(x \normalsize\color{red }{ +~\rm{c}) } &~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= bx ~~~~\rm{\Rightarrow}~~~~ g(x)= bx \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= bx ~~~~\rm{\Rightarrow}~~~~ g(x)= bx \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)

Answer 3

this is a rule for shifting a line f(x)=bx any direction. (where b is the coefficient of x).

Answer 4

in your case this coefficient is 1.
And this, your shift left from \(\large\color{slate}{ y=1x }\) would be
\(\large\color{slate}{ y=1(x+c) }\)

and the shift up would be \(\large\color{slate}{ y=1x+c }\)

bt you know that \(\large\color{slate}{ y=1x+c }\) is same as \(\large\color{slate}{ y=1(x+c) }\) as you expand the parenthesis.

Answer 5

And same way it happens when you have a shift light and shift down in this case, are same.

to the right by c units.
\(\large\color{slate}{ y=1(x-c ) }\)

down by c units
\(\large\color{slate}{ y=1x-c }\)
As you expand the parenthesis, \(\large\color{slate}{ y=1(x-c) }\) is same as \(\large\color{slate}{ y=1x-c }\) and