The parent function [tex]f(x)=x[/tex] produces the straight line called line of odd quadrants that is symmetric relative to x & y axis.
The function [tex]g(x)=x+5[/tex] which can be rewritten as [tex]g(x)=f(x)+5[/tex] produces outputs always by 5 larger (shifts parent function up the y-axis by 5) than parent function however it's slope does not change the slope and the symmetry has vanished.
Hope this helps.
