suppose f[x]=x^3. Find the graph of f [x+5]

Question

anonymous · Answer

PLEASE HELP

anonymous · Answer

$$f(x)=x^3\
f(x+5)=(x+5)^3$$

solomonzelman · Answer

$\huge\color{ royalblue }{\large {\bbox[5pt, lightyellow  ,border:2px solid  white  ]{   \large\text{ }\
\begin{array}{|c|c|c|c|}
\hline \rm{ Shifts ~~~from~~~ f(x)~~~ to~~~g(x)}&~\rm{c~~~units~~~~}	\
\hline 
					\f(x)=  x^3    ~~~~~\rm{\Rightarrow}~~~~  g(x)= (x \normalsize\color{red}{  -~\rm{c} })^3  &~\rm{to~~the~~right~}				\
\text{ }					\
	f(x)=  x^3     ~~~~~\rm{\Rightarrow}~~~~     g(x)= (x \normalsize\color{red}{  +~\rm{c} })^3&~\rm{to~~the~~left ~}					\
\text{ }					\
	f(x)=  x^3     ~~~~~\rm{\Rightarrow}~~~~     g(x)=  x^3 \normalsize\color{red}{  +~\rm{c}   } &~\rm{up~}					\
\text{ }					\
	f(x)=  x^3     ~~~~~\rm{\Rightarrow}~~~~     g(x)=  x^3 \normalsize\color{red}{  -~\rm{c}   } &~\rm{down~}		\					\
\hline
\end{array}  }}}$

solomonzelman · Answer

so your function is the shift to the left, by 5 units.