Question

Im having trouble understanding what this question is asking for exactly? Can anyone help explain?

If a function, f(x) is shifted to the left four units, what will the transformed function look like?

Answer 1

what is your f(x), (your function), is it given to you?

Answer 2

It doesn't give you a function that's the thing, it just says "if a function" in general.

Answer 3

Ohh, so I will give you a couple of examples, of a shift in a function.

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

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

Answer 4

you are adding "c" for a shift of c units to the left,
so to speak, "inside the parenthesis"

see?

Answer 5

So they are asking you to say, (I think) that you would add +4 into every x.
YOu know what I mean, right.
It will be f(x+4), yes?

Answer 6

That seems to make sense from the video I was watching. I didn't know if that's what they were asking for or not though. So I would just right f(x)+4?

Answer 7

yes. I think...

Answer 8

https://www.khanacademy.org/math/algebra2/functions_and_graphs/shifting-reflecting-functions/v/shifting-and-reflecting-functions