Give an example of a function that is not strictly increasing. Draw its graph and prove that the function is not strictly increasing

Question

I picked x^4 to be a function which is not strictly increasing for all real numbers.

Since to be not strictly increasing means that for the function y=f(x)

x1 < x2 then f(x1)< f(x2)

but I get stuck, Im not sure how to go about proving this.

Answer 1

Ok,f(x) = x sin(1/x) on R will do nicely and geometrically.

The function osillates wildly and obviously cannot be strictly increasing.A rigorous proof is easy,you can almost do it from the picture.