ok but then il try say for x=1 and y=2 i find f(x+y) not equal
to f(x)+f(y) which makes 10 not equal 14. so this is not linear
also? can someone give me an example of a linear function that
works. ......... wait so the these properties cannot be
satisfied if there is a constant, but i thought a linear
function could be plotted y=mx+b im confused But Linear Algebra
uses a more stringent definition for "linear transformation"- we
must have f(x+ y)= f(x)+ f(y) and f(ax)= af(x). As I said above,
the only "linear" functions in that sense, from R to R are of
the form f(x)= ax for some number a.