Question

Graph y = |x + 2| and give domain and range

Answer 1

Rules of \(\large\color{black}{ \rm shifts }\) from \(\large\color{black}{ \rm f(x) }\) to \(\large\color{black}{ \rm g(x) }\).


\(\large\color{black}{ \rm f(x)=\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=\left| x \color{blue}{ -~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm {c} }\) units to the \(\normalsize\color{blue}{ \rm right }\).


\(\large\color{black}{ \rm f(x)=\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=\left| x \color{blue}{ +~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm {c} }\) units to the \(\normalsize\color{blue}{ \rm left }\).


\(\large\color{black}{ \rm f(x)=\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=\left| x \right| \color{blue}{ +~\rm{c} }}\)
\(\large\color{blue}{ ~\rm {c} }\) units \(\normalsize\color{blue}{ \rm up }\).


\(\large\color{black}{ \rm f(x)=\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=\left| x \right| \color{blue}{ -~\rm{c} }}\)
\(\large\color{blue}{ ~\rm{c} }\) units \(\normalsize\color{blue}{ \rm down }\).

So you know how your function is shifted, right?

Answer 2

For the domain, we don't see any restrictions, do we?
And for the range, we know an absolute value has to be equal to 0 or to a greater number, but not to a negative.

Answer 3

No, not really.

Answer 4

you see you added 2 into the absolute value, so look at the rule number 2. What is done to your graph?

Answer 5

Im completely confused

Answer 6

y = |x `+ 2`| see the gray part?

Answer 7

Look at rule, 2 where you add +C into the absolute value.