A linear function is defined as:

#f(x)=a*x+b#

Note that is has two parameter - the #a#, which multiplies the variable x, and the constant #b#. There are no powers or roots in this function. Adding any kind of power to this expression will make it turn into a curve. Some examples of nonlinear functions:

#y=x^2+1#.

#y=e^x+1#.

#y=ln(x)#, where #x>0#.

#y=1/x#, which is the same as #y=x^(-1)# and #x!=0#.

#y=sqrt(x)#, which is the same as #y=x^(1/2)# and #x>=0#.

Therefore, if we add any power to #x# or place it in a logarithm or under a division, the result will be a curve. Also, the function cannot be linear if it has a restriction at its domain or range.