Question

will give medal
and will fan if you help!

Consider the function f(x) = x^2 and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)?

g(x) = f(x) + 2 = x^2 + 2

Answer 1

a. The graph of g(x) is the graph of f(x) shifted up 2 units.

b. The graph of g(x) is the graph of f(x) shifted down 2 units.

c. The graph of g(x) is the graph of f(x) shifted to the right 2 units.

d. The graph of g(x) is the graph of f(x) shifted to the left 2 units.

Answer 2

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

Answer 3

this is an example, of a rule of how to shift.

Answer 4

do you get what solomonZelman is trying to show you

Answer 5

kind of, but not fully. @Percy*

Answer 6

'c' is any constant
it can be '2'

Answer 7

(or any real, positive or negative number)
giving it a notation \(\large\color{blue}{ \displaystyle \left\{ c\in {\bf R}\right\} }\)
(i.e 'c' is a real number)

Answer 8

For example, if you say
\(\large\color{black}{ \displaystyle x^2+\color{red}{3} }\)
that is a 3 unit shift up from \(\large\color{black}{ \displaystyle x^2}\)

Answer 9

now, what if that red 3 was a two?

Answer 10

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

Answer 11

again, this '3' in your case is '2'
so same rules apply, but you are shifting 2 units whatever way (not 3)

Answer 12

if you have question(s), ask pliz.

Answer 13

thanks a lot!

Answer 14

big help

Answer 15

sure.... you are always welcome!