About one-third of a standard Algebra class involves creating equivalent expressions. By using a functions-based approach we can have students make sense of how expressions that don't look alike -- e.g., 4x and 2x + 2x or (x+2)(x-3) and x^2-x-6 -- are the SAME (equivalent).
Leaving f(x) = 4x, enter functions into g(x), h(x), etc. that are the SAME as 4x. How can we tell from the graph if they are the same? What happens if they are not the same?
Optional: Change f(x) = 4x to f(x) = 4sin(x). See if you can use patterns from finding functions that are the same as 4x to find functions that are the same as 4sin(x).