Question

State the various transformations applied to the base function f(x)=√x to obtain a graph of the function g(x)= √x+5 -4

Answer 1

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

Answer 2

\(\large\color{black}{ g(x)=\sqrt{x+5}-4 }\) is your function.

here I'll label everything for you.

\(\large\color{black}{ g(x)=\sqrt{x\color{red}{+5}}\color{green}{-4} }\)

the \(\large\color{black}{ \color{red}{\rm red} }\) is a shift left.
the \(\large\color{black}{ \color{green}{\rm green} }\) is a shift down.

(refer to the chart I posted above)

Answer 3

have any questions?

Answer 4

no i understand now Thank you

Answer 5

You are welcome!

Answer 6

if you want I can make a bigger chart next time, lol:)