Algebraically determine if the relation y=10x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry

Question

Algebraically determine if the relation y=10x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry

Answer 1

A graph of a function y = f(x) is symmetric with respect to the origin if replacing x by -x and y by -y yields the same function.  For y = 10x, if we replace x by -x and y by -y, we get -y = -10x, which simplifies to y = 10x.  Thus, the graph of y = 10x is symmetric with respect to the origin.    

Answer 2

Linear functions are odd degree functions.  These type of functions do not have any symmetry with respect to the either axis.

 

 

However, the function       y=mx+b

 

where   m = ±1

            b = 0

 

does have symmetry with respect to the origin.