Injective and Surjective Functions 1

This worksheet explores the injectivity and surjectivity of the function $f(x)=\sin(x)$. As a function $f:\mathbb{R}\to\mathbb{R}$, it is neither injective nor surjective. But by carefully restricting the domain and codomain, we can define a new function that is either injective, or surjective, or both.

[list=1] [*] Adjust [color=#0000ff]$a$[/color] and [color=#0000ff]$b$[/color] to restrict the domain of $f$ to an interval on which it is injective. [*] Adjust [color=#ff0000]$c$[/color] and [color=#ff0000]$d$[/color] to restrict the codomain of $f$ to an interval on which it is surjective. [/list]