Use the graph of

to determine if the following statement is true or false.

$\backslash$definecolor$\{$cbred$\}\{$HTML$\}\{$D$55$E$00\}$

$\backslash$definecolor$\{$cborange$\}\{$HTML$\}\{$E$69$F$00\}$

$\backslash$definecolor$\{$cbyellow$\}\{$HTML$\}\{$F$0$E$442\}$

$\backslash$definecolor$\{$cbgreen$\}\{$HTML$\}\{09$BF$8$E$\}$

$\backslash$definecolor$\{$cbblue$\}\{$HTML$\}\{0072$B$2\}$

$\backslash$definecolor$\{$cbgray$\}\{$HTML$\}\{$CCCCCC$\}$

$\backslash$begin$\{$tikzpicture$\}$

$\backslash$begin$\{$axis$\}[$

width $=10$cm$,$

height $=10$cm$,$

xtick $=\{0,...,6\},$

ytick $=\{-6,...,6\},$

tick label style$=\{$font$=\backslash$footnotesize$\},$

xmin $=-0\mathrm{.}25,$ xmax $=6\mathrm{.}25,$

ymin $=-0\mathrm{.}25,$ ymax $=6\mathrm{.}25,$

axis x line $=$ center,

axis y line $=$ center,

axis line style $=\{$black$,$ thick$\},$

xlabel$=\{$$x$$\},$

ylabel$=\{$$y$$\},$

grid style $=\{$cbgray$,$thick$\},$

grid$=$both,

minor tick num$=1,$

disabledatascaling$]$

$\backslash$addplot$[$cbblue$,$ultra thick,$-$latex$](1,1)$ to $(0,0)$;

$\backslash$addplot$[$cbblue$,$fill$=$white,ultra thick$](1,1)$ circle$[$radius$=2\mathrm{.}5$pt$]$;

$\backslash$addplot$[$cbblue$,$domain$=1$:$4,$ultra thick,samples$=100]\{1+($x$-3)^2/2\}$;

$\backslash$addplot$[$cbblue$,$fill$=$cbblue,ultra thick$](1,3)$ circle$[$radius$=2$pt$]$;

$\backslash$addplot$[$cbblue$,$fill$=$white,ultra thick$](3,1)$ circle$[$radius$=2\mathrm{.}5$pt$]$;

$\backslash$addplot$[$cbblue$,$fill$=$cbblue,ultra thick$](3,4)$ circle$[$radius$=2$pt$]$;

$\backslash$addplot$[$cbblue$,$ultra thick,$-$latex$](4,1\mathrm{.}5)$ to $(5,2)$ to $(6,6)$;

$\backslash$draw $(1,6)$ node$[$anchor$=$north west,rectangle,fill$=$white$]\{\backslash$textcolor$\{$cbblue$\}\{\backslash$boldmath$y$=$f$($x$)$$$\}\}$;

$\backslash$end$\{$axis$\}$

$\backslash$end$\{$tikzpicture$\}$

The function

admits a continuous correction at x$=3$

$.$