Question

FAN AND MEDAL
what is the equation of the blue function if the red function is f(x) = log(x)

Answer 1

can you visualize the shift?
which directions and by how much is the blue function shifted from the red function?

Answer 2

its up one unit and left one unit, but i dont know how to write that in function form lol

Answer 3

yes, it is up one unit and left 1 unit. Can I give you a couple of examples of shift of a function in general?

Answer 4

f(x) = log(x)+1 makes the function go up a unit, but the left i dont know how to do

Answer 5

sure, go ahead

Answer 6

Example 1
\(\large\color{ blue }{\large {\bbox[5pt, lightyellow ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline \texttt{Shifts} ~~~\tt from~~~ {f(x)~~~\tt to~~~g(x)}&~\tt{c~~~units~~~~} \\
\hline
\\f(x)= \sqrt[4]{x} ~~~~\rm{\Rightarrow}~~~~ g(x)= \sqrt[4]{x \normalsize\color{red }{ -~\rm{c}} } &~\rm{to~~the~~right~} \\
\text{ } \\
f(x)= \sqrt[4]{x} ~~~~\rm{\Rightarrow}~~~~ g(x)= \sqrt[4]{x \normalsize\color{red}{ +~\rm{c}} } &~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= \sqrt[4]{x} ~~~~\rm{\Rightarrow}~~~~ g(x)= \sqrt[4]{x} \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= \sqrt[4]{x} ~~~~\rm{\Rightarrow}~~~~ g(x)= \sqrt[4]{x} \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)



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

Answer 7

but what happens when you have log in there?

Answer 8

log(x+1) +1
?

Answer 9

so, it would be same, you are adding for a shift to the left inside the parenthesis,
and adding just to the left side for a vertical shift up.

Answer 10

is f(x) = log (x+1) +1 correct?

Answer 11

Yes, that would be 1 unit left and 1 unit up;)

Answer 12

gracias

Answer 13

you welcome